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CHAPTER 11 Oscillations and Waves
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1. Which of the following expressions does not represent SHM?
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(a) Acosωt
(b) Asin 2ωt
(c) Asinωt+b cosωt
(d) Asin2 ωt
2. The bob of simple pendulum having length l, is displaced from mean position to an angular position q with respect to vertical. If it is released, then velocity of bob at equilibrium position
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(a) √2 1 gl( c − osθ )
(b) √2gl( 1 +cosθ )
(c)√ 2gl cosθ
(d)√ 2gl
3. A simple harmonic motion having an amplitude A and time period T is represented by the equation y t = ( 5 4 sin ) π + m Then the values of A (in m) and T (in sec) are
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(a) A = 5; T = 2
(b) A = 10; T = 1
(c) A = 5; T = 1
(d) A = 10; T = 2
4. If the maximum velocity and acceleration of a particle executing SHM are equal in magnitude, the time period will be
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(a) 1.57 seconds
(b) 3.14 seconds
(c) 6.28 seconds
(d) 12.56 seconds
5. How long after the beginning of motion is the displacement of a harmonically oscillating po half its amplitude, if the period is 24 seconds and initial phase is zero?
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(a) 12 seconds
(b) 2 seconds
(c) 4 seconds
(d) 6 seconds
6. A particle is executing SHM with amplitude A and has maximum velocity Vo . Its speed at displacement A/2 will be
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(a) ( √ 3)Vo/ 2
(b) Vo / √2
(c) Vo
(d) Vo /4
7. A particle under the action of a SHM has a period of 3 seconds and under the effect of another it has a period 4 seconds. What will be its period under the combined action of both the SHM’s in the same direction?
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(a) 7 seconds
(b) 5 seconds
(c) 2.4 seconds
(d) 0.4 seconds
8. The displacement x of a particle in motion is given in terms of time by x x( ) − = 4 1− 5cos .
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(a) The particle executes SHM.
(b) The particle executes oscillatory motion which is not SHM.
(c) The motion of the particle is neither oscillatory nor simple harmonic.
(d) The particle is not acted upon by a force when it is at x = 4.
9. The equation of SHM is given as x t = + 3 2 sin c 0 4 π π os 20 t, where x is in cms and t is in seconds. The amplitude is
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(a) 7 cm
(b) 4 cm
(c) 5 cm
(d) 3 cm
10. What should be the displacement of a simple pendulum whose amplitude is A, at which potential energy is 1 4 th of the total energy?
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(a) A /√2
(b) A /2
(c) A /4
(d) A /2√2
11. A particle is executing SHM with amplitude A and has a maximum velocity Vo . The displacement at which its velocity will be (Vo /2) and the velocity at displacement A/2 are
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(a) A / 2 , V o /2
(b) A /3 , Vo/3
(c) (√3 /2)A, √3V/2
(a) A / √2 , V o /√2
12. A particle executes simple harmonic motion between x = -A and x = +A. The time taken for it to go from 0 to A/2 is T1 and to go from A/2 to A is T2 . Then
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(a) T1 < T2
(b) T1 > T2
(c) T1 = T2
(d) T1 = 2T2
13. A body executes simple harmonic motion under the action of a force F1 with a time period (4/5) seconds. If the force is changed to F2 it executes SHM with time period (3/5) seconds. If both the forces F1 and F2 act simultaneously in the same direction on the body, its time period (in seconds) is
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(a) 12/25
(b) 24/25
(c) 35/24
(d) 25/12
14. The potential energy of a particle of mass 1 kg in motion along the x-axis is given by U = 4(1 - cos 2x) J, where x is in metres. The period of small oscillations (in second) is
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(a) 2π
(b) π
(c) π /2
(d) √2π ⋅
15. A particle executing SHM while moving from one extremity is found at distances x1 , x2 and x3 from the centre at the end of three successive seconds. The time period of oscillation is
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(a) 2π θ/
(b) π /θ
(c) θ
(d) π /2θ
17. The equation of motion of a particle executing simple harmonic motion is a x + = 16 0 2 π . In this equation, a is the linear acceleration in m/s2 of the particle at a displacement x in metre. The time period in simple harmonic motion i
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(a) 1/4 second
(b) 1/2 second
(c) 1 second
(d) 2 seconds
18. The x-t graph of a particle undergoing simple x (cm) harmonic motion is shown below. The acceleration of the particle at t = 4 3 s is
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(a) √3 / 32 π2 cm/s2
(b) −π2 /32 cm/s2
(c) π2 /32 cm/s2
(d) -√3 / 32 π2 cm/s2
19. If < > T U and < > denote the average kinetic and the average potential energies respectively of a mass executing a simple harmonic motion, over one period, then the corresponding relation is
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(a) < T U >=− 2 < >
(b) < T U >=+ 2 < >
(c) < > T U = < >
(d) < > U T = < 2 >
20. The maximum displacement of the particle executing SHM is 1 cm and the maximum acceleration is 1.57 cm/s2 . Its time period is
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(a) 0.25 s
(b) 4.0 s
(c) 1.57 s
(d) 3.14 s
21. Time period of a simple pendulum is T. If its length increases by 2%, the new time period becomes
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(a) 0.98 T 1
(b) 1.02 T
(c) 0.99 T
(d) 1.01 T
22. If x, v and a denote the displacement, the velocity and the acceleration of a particle executing simple harmonic motion of time period T, then, which of the following does not change with time?
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(a) a2 T2 + 4π2 v2
(b) aT / x
(c) aT = 2π v
(d) aT /v
23. The total energy of a particle executing simple harmonic motion is proportional to
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(a) displacement from equilibrium position
(b) frequency of oscillation
(c) velocity of equilibrium position
(d) square of amplitude of motion
24. If a simple pendulum of length l has maximum angular displacement q, then the maximum kinetic energy of the bob of mass m is
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(a) (1 /2) / m √l/ g
(b) (1/2)(mg/l)
(c) mgl( 1− cosθ)
(d) ( / 1 2) s mgl sinθ
25. A simple pendulum consisting of a ball of mass m tied to a string of length l is made to swing on a circular arc of angle q in a vertical plane. At the end of this arc, another ball of mass m is placed at rest. The momentum translated to this ball at rest by the swinging ball is
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(a) zero
(b) mθ /√l / g
(c) m l θ / √lg
(d) m/2 √l /g
26. For a particle executing simple harmonic motion, the kinetic energy K is given by K K t = o cos . 2 ω The maximum value of potential energy is
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(a) Ko
(b) zero
(c) Ko/2
(d) not obtainable
27. A simple pendulum suspended from the ceiling of a train has a period T when the train is at rest. When the train is accelerating with a uniform acceleration, the time period of the simple pendulum will
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(a) decrease
(b) increase
(c) remain unchanged
(d) become infinite
28. A simple pendulum is set up in a trolley which moves to the right with an acceleration a on the horizontal plane. Then, the thread of the pendulum in the mean position makes an angle q with the vertical given by
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(a) tan-1 (a/g) in the forward direction
(b) tan-1 (a/g) in the backward direction
(c) tan-1 (g/a) in the backward direction
(d) tan-1 (g/a) in the forward direction
29. A heavy brass sphere is hung from a spring and it executes vertical vibrations with period T. The sphere is now immersed in a non-viscous liquid with a density (1/10)th that of brass. When set into vertical vibrations with the sphere remaining inside liquid all the time, the time period will be
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(a) √9 /1 0T
(b) √10/9T
(c) (9/10)T
(d) unchanged
30. A smooth inclined plane having angle of inclination of 30º with the horizontal has a 2.5 kg mass held by a spring which is fixed at the upper end. If the mass is taken 2.5 cm up along the surface of the inclined plane, the tension in the spring reduces to zero. If the mass is now released, the angular frequency of oscillation is
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(a) 7
(b) 14
(c) 0.7
(d) 1.4
31. Two pendulums of lengths 121 cm and 100 cm start vibrating. At some instant the two are in the mean position in the same phase. After how many vibrations of the shorter pendulum the two will be in phase in the mean position? n
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(a) 10
(b) 11
(c) 20
(d) 21
32. A pendulum bob carries a -ve charge -q. A positive charge +q is held at the point of support. Then, the time period of the bob is
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(a) greater than 2π √L /g
b) less than 2π √L /g
(c) equal to 2π √L /g
(d) equal to 2 2 π √L /g
33.Two masses MA and MB are hung from two strings of length l A and l B respectively. They are executing SHM with frequency relation f A = 2f B, then relation
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(a) l A = lB / 4 , does not depend on mass
(b) lA = 4lB, does not depend on masstion 2
(c) lA = 2lB and MA = 2MB
(d) l A=lB/2 and MA= MB/2
34. A simple pendulum has time period T1 . The point of suspension is now moved upward according to the relation y = kt2 (k = 1 m/s2 ), where y is the vertical displacement. The time period now becomes T2 . The ratio of T T 1 2 2 2 / is (Take g = 10 m/s2 )
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(a) 6/5
(b) 5/6
(c) 1
(d) 4/5
35. A simple pendulum of length L has an energy E and amplitude A. The energies of the simple pendulum (i) when the length is doubled but with same amplitude and (ii) when the amplitude is doubled but with the same length, are respectively
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(a) 2E, 2E
(b) E2 , E/2
(c) E/2 , 2E
(d) E/2 , 4E
36. A pendulum has period T for small oscillations. An obstacle is placed directly beneath the pivot, so that only the lowest one quarter of the string can follow the pendulum bob when it swings in the left of its resting position as shown in the figure. The pendulum is released from rest at a certain point A. The time taken by it to return to that point is
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(a) T
(b) T/2
(c) 3T/4
(d) T/4
37. Which of the following characteristics does not change due to the damping of simple harmonic motion?
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(a) Angular frequency
(b) Time period
(c) Initial phase
(d) Amplitude
38. The equations of two waves acting in perpendicular direction are given as x a = + cos (ω δ t y ) c and a = + os( ) ω α t , whereδ = + α π 2 , the resultant wave represents
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(a) a parabola
(b) a circle
(c) an ellipse
(d) a straight line
39. Two masses m1 and m2 are suspended together by a massless spring of constant k. When the masses are in equilibrium, m1 is removed without disturbing the system; the amplitude of vibration is
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(a) m1 g/k
(b) m2 g/k
(c) ( m1 + m2 /k)g
(d) ( m2 + m1/k)g
40. A hollow sphere filled with water forms the bob of a simple pendulum. A small hole at the bottom of the bob allows the water to slowly flow out as it is set into oscillations of small amplitude and its period of oscillation is measured. The time period will
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(a) first increase then decrease
(b) remains constant
(c) decrease
(d) increase
41. A particle vibrates in SHM along a straight line. Its greatest acceleration is 5 2 2 π cm s− and when its distance from the equilibrium position is 4 cm, the velocity of the particle is 3 2 2 π cm s− .The amplitude and the period of oscillation of the vibrating particle is
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(a) 10 cm, 4 seconds
(b) 5 cm, 2 seconds
(c) 5 cm, 4 seconds
(d) 10 cm, 2 seconds
42. In the arrangement, spring constant k has value 2 N m-1 , mass M = 3 kg and mass m = 1 kg. Mass M is in contact with a smooth surface. The coefficient of friction between two blocks is 0.1. The time period of SHM executed by the system is
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(a) π √6
(b) π √2 ⋅
(c) 2 √2π
(d) 2p
43. A particle of mass m is attached to three identical springs A, B and C each of force constant k as shown in figure. If the particle of mass m is pushed slightly against the spring A and released, then the time period of oscillation is
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(a) 2 π √2m/k
(b) 2 π √m/2k
(c) 2π √m/k
(d) 2π √m/3k
44. A uniform circular disc of mass 12 kg is held by two identical springs as shown in the figure. When the disc is pressed down slightly and released, it executes SHM with a time period of 2 seconds. The force constant of each spring is
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(a) 236 N/m
(b) 118.3 N/m
(c) 59.15 N/m
(d) None of these
45. To make the frequency double of an oscillator, we have to
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(a) double the mass
(b) half the mass
(c) quadruple the mass
(d) reduce the mass to one-fourth
46. Two identical springs of constant k are connected in series and parallel as shown in the figure. A mass M is suspended from them. The ratio of their frequencies of vertical oscillations will be
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(a) 2 : 1
(b) 1 : 2
(c) 1 : 4
(d) 4 : 1
47. When a body of mass 1.0 kg is suspended from a certain light spring hanging vertically, its length increases by 5 cm. By suspending 2.0 kg block to the spring and if the block is pulled through 10 cm and released, the maximum velocity of it (in m/s) is
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(a) 0.5
(b) 1
(c) 2
(d) 4
48. A block of mass m compresses a spring of stiffness k through a distance l/2 as shown in the figure. If the block is not fixed to the spring, the period of motion of the block is
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(a) 2π √m/k
(b)(π + 4)√m/k
(c) (1+π) √m/ k
(d) None of these
49. Two identical particles each of mass m are interconnected by a light spring of stiffness k, the time period for small oscillation is equal to
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(a) 2π√m/k
(b) π√ m/k
(c) 2π √m/2k
(d) π√2m/k
50. In the given diagram, S1 and S2 are identical springs. The frequency of oscillation of the mass m is f. If one of the springs is removed, the frequency will be
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(a) f
(b) 2f
(c)√ 2 f
(d) f / √2
51. An object on a spring vibrates in simple harmonic motion at a frequency of 4.0 Hz and an amplitude of 8.0 cm. If the mass of the object is 0.20 kg, the spring constant is
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(a) 40 N/m
(b) 87 N/m
(c) 126 N/m
(d) 160 N/m
52. An electric motor of mass 40 kg is mounted on four vertical springs each having spring constant of 4000 N/m. The period with which the motor vibrates vertically is
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(a) 0.314 s
(b) 3.14 s
(c) 0.628 s
(d) 0.157 s
53. Two SHM’s are respectively represented by y = asin (wt - kx) and y b = − cos (ωt kx).The phase difference between the two is
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(a) p/2
(b) p/4
(c) p/6
(d) 3p/4
54. Two particles P and Q describe SHM of same amplitude a and frequency ν along the same straight line. The maximum distance between two particle is 2a. The initial phase difference between the particles is
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(a) zero
(b) π /2 ⋅
(c) π /6
(d) π /3
55. A particle is subjected to two mutually perpendicular simple harmonic motions such that its x and y coordinates are given by x = 2 sin wt y t = + 2 4 sin ω π The path of the particle will be
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(a) an ellipse
(b) a straight line
(c) a parabola
(d) a circle
56. Two simple harmonic motions with same frequency act on a particle at right angles, i.e., along x and y-axis. If the two amplitudes are equal and the phase difference is π /2 the resultant motion will be
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(a) a straight line inclined at 45º to the x-axis.
(b) an ellipse with the major axis along the x-axis.
(c) an ellipse with the major axis along the y-axis.
(d) a circle
57. If two SHMs are represented by equations y t 1 10 3 4 = + sin π π and y t t 2 = + 5 3 [sin ( ) π π 3 3 cos ( )], the ratio of their amplitudes is
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(a) 2 : 1
(b) 1 : 2
(c) 1 : 1
(d) 1:√ 2
58. Which of the following combinations of Lissajous’ figure will be like infinite ( ) ∞ ?
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(a) x a = = sin , ω ω t y b t sin
(b) x a = = sin , 2ω ω t y b t sin
(c) x a = = sin , ω ω t y b t sin 2
(d) x a = = sin , 2 2 ω ω t y b t
59. A particle is subjected simultaneously to two SHM’s, one along the x-axis and the other along the y-axis. The two vibrations are in phase and have unequal amplitudes. The particle will ex
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(a) straight line motion
(b) circular motion
(c) elliptic motion
(d) parabolic motion
60. Which of the following statements is correct?
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(a) Both sound and light waves in air are longitudinal.
(b) Both sound and light waves in air are transverse.
(c) Sound waves in air are transverse while light longitudinal.
(d) Sound waves in air are longitudinal while light waves transverse
61. Of the following properties of a wave, the one that is independent of the other is its
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(a) amplitude
b) velocity
(c) wavelength
(d) frequency
62. Which of the following properties of a wave does not change with a change in medium?
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(a) Frequency
(b) Wavelength
(c) Velocity
(d) Amplitude
63. It is possible to distinguish between transverse and longitudinal waves by studying the property o
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(a) interference
(b) diffraction
(c) reflection
(d) polarization
64. The particles of a medium vibrate about their mean positions whenever a wave travels through that medium. The phase difference between the vibrations of two such particles
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(a) varies with time
(b) varies with distance separating them
(c) varies with time as well as distance
(d) is always zero
65. The angle between particle velocity and wave velocity in a transverse wave is
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(a) zero
(b) p/4
(c) p/2
(d) p
66. A heavy rope is suspended from a rigid support. A wave pulse is set up at the lower end; then
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(a) the pulse will travel with uniform speed.
(b) the pulse will travel with increasing speed.
(c) the pulse will travel with decreasing speed.
(d) the pulse cannot travel through the rope.
67. Define Mach Number.
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(a) It is the ratio of the stress to strain.
(b) It is the ratio of the strain to stress.
(c) It is the ratio of the velocity of an object to the velocity of sound.
(d) It is the ratio of the velocity of sound to the velocity of an object
68. Which one of the following does not represent a travelling wave?
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(a) y= ym f( x-vt)
(b) y =ym sin k(x +vt)
(c) y =ym log (x-vt )
(d) y= f (x2-vt2 )
69. Which of the following equations represents a wave?
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(a) y = a(wt - kx)
(b) y = a sin wt
(c) y = a cos kx
(d) y = a sin (at - bx + c)
70. A plane sound wave is travelling in a medium. With reference to a frame A, its equation is y = a cos (wt - kx). With reference to a frame B, moving with a constant velocity v in the direction of propagation of the wave, equation of the wave will be
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(a) y = a cos [(w + kv)t - kx]
(b) y = -a cos [(w - kv)t - kx]
(c) y = -a cos [(w - kv)t - kx]
(d) y = a cos [(w + kv)t + kx
71. In a sine wave, the position of different particles at time t = 0 is shown in the figure. The equation for this wave if it is travelling along positive x-axis can be
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(a) y A = − sin (ωt kx)
(b) y A = − sin (kx ωt)
(c) y A = − cos (ωt kx)
(d) y A = − cos (kx ωt)
72. A transverse wave is travelling in a string. Equation of the wave
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(a) is not equal to the shape of the string at an instant t.
(b) is general equation for displacement of a particle of the string.
(c) must be sinusoidal equation.
(d) is an equation for displacement of the particle of one end only.
73. A wave equation which gives the displacement along Y-direction is given y t = + 10 60 2x 4 sin ( ) where, x and y are in metre and t in sec. Among the following choose the correct statement
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(a) It represents a wave propagating along positive x-axis with a velocity of 30 m/s.
(b) It represents a wave propagating along negative x-axis with a velocity of 120 m/s.
(c) It represents a wave propagating along negative x-axis with a velocity of 30 m/s.
(d) It represents a wave propagating along negative x-axis with a velocity of 104 m/s.
74. If the equation of a progressive wave is given by y t x = − + 4 5 9 6 sinπ π Then, which of the following is correct?
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(a) v = 5 cm/s
(b) λ =18 m
(c) A = 0.04 cm
(d) f = 50 Hz
75. The equation for the displacement of a stretched string is given by y where, y and x are in cm and t in second. The (i) frequency (ii) velocity of the wave (iii) maximum particle velocity are
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(a) 50 Hz, 50 m/s, 20p m/s
(b) 50 Hz, 20 m/s, 50 m/s
(c) 50 Hz, 50 m/s, 2p m/s
(d) 50 Hz, 50 m/s, 4p m/s
76. A wave is represented by the eqautionsin . π π where, x is in metres and t in seconds. The speed of the waves is
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(a) ( 175π) m/s⋅
(b) ( 49π )m/s⋅
(c) ( / 49 π )m/s
(d) ( . 0 28π )m/s⋅
77. The speed of a wave in a medium is 650 m/s. If 4000 waves are passing through a point in the medium in 1.67 minutes, then its wavelength will be
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(a) 25.16 m
(b) 16.25 m
(c) 32.50 m
(d) 8.25 m
78. The amplitude of a wave disturbance propagating in the positive Y-direction is given by y at and at s [ ( ) ] where, x and y are in m. If the shape of the wave disturbance does not change during the propagation, what is the velocity of the wave?
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(a) 1 m/s
(b) 1.5 m/s
(c) 0.5 m/s
(d) 2 m/s
79. The total energy of particle performing SHM depend on
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(a) k, a, m
(b) k, a
(c) k, a, x
(d) k, x
80. A simple harmonic wave is represented by the relation If the maximum particle velocity is three times the wave velocity, the wavelength l of the wave is
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(a) π ao /3 ⋅
(b) 2 3 π ao / ⋅
(c) πao
(d) π ao /2
81. The equation y of a simple harmonic wave gives us
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(a) the displacement of all particles of the medium at a particular instant of time only.
(b) the displacement of a single particle at any time.
(c) the displacement of all the particles of the medium at a particular instant of time as well as the displacement of a single particle at any time.
(d) the behaviour of the medium as a whole.
82. The diagram below shows the propagation of a wave. Which points are in phase?
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(a) AB
(b) BC
(c) BD
(d) EB
83. A wave equation is y t = + x − 10 60 2 4 sin ( ), where, x and y are in metres and t is in second. Which of the following statements is correct?
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(a) The wave travels with a velocity of 300 m/s in the negative direction of the x-axis.
(b) Its wavelength is p metre.
(c) Its frequency is 50p hertz.
(d) All of these
84. A simple harmonic progressive wave is represented by the equation y x = − 8 2 sin ( π 0 1. ) 2t where, x and y are in cm and t is in seconds. At any instant the phase difference between two particles separated by 2.0 cm in the X-direction is
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(a) 18°
(b) 54°
(c) 36°
(d) 72°
85. A travelling wave in a gas along the positive X-direction has an amplitude of 2 cm, velocity 45 m/s and frequency 75 Hz. Particle acceleration after an interval of 3 seconds at a distance of 135 cm from the origin is
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(a) 0.44 × 102 cm/s2
(b) 4.4 × 105 cm/s2
(c) 4.4 × 103 cm/s2
(d) 44 × 105 cm/s2
86. The speed of a wave in a certain medium is 960 m/s. If 3600 waves pass over a certain point of the medium in 1 minute the wavelength is
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(a) 2 metre
(b) 8 metre
(c) 4 metre
(d) 16 metre
87. The phase difference between two points separated by 0.8 m in a wave of frequency 120 Hz is 0.5p. The wave velocity is
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(a) 144 m/s
(b) 256 m/s
(c) 384 m/s
(d) 720 m/s
88. Two waves having equation x1 = asin (wt - kx + f1 ), x2 = asin (wt - kx + f2 ). If in the resultant wave the frequency and amplitude remains equals to amplitude of superimposing waves, the phase difference between them is
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(a) π/6
(b) 2π/3
(C) π/4
(d) π/3
89. The equation of a wave is represented by y t x 10 100 10 4 sin m, then the velocity of wave will be
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(a) 100 m/s
(b) 4 m/s
(c) 1000 m/s
(d) 10 m/s
90. In a plane progressive harmonic wave particle speed is always less than the wave speed if
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(a) amplitude of wave < λ/2p
(b) amplitude of wave > λ/2p
(c) amplitude of wave < λ
(d) amplitude of wave > λ/p
91. When an oscillator completes 100 oscillations its amplitude reduced to 1/3 of initial value. What will be its amplitude, when it completes 200 oscillations?
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1 point
(a) 1/8
(b) 2/3
(c) 1/6
(d) 1/9
92. A sine wave has an amplitude A and wavelength l. The ratio of particle velocity and the wave velocity is ( )
*
1 point
(a) ≤1
(b) = 1
(c) ≥1
(d) None of these
93. Two points on a travelling wave having frequency 500 Hz and velocity 300 m/s are 60° out of phase, then the minimum distance between the two points is
*
1 point
(a) 0.2
(b) 0.1
(c) 0.5
(d) 0.4
94. The equation of a wave travelling on a string is , where x, y are in cm and t in second. The velocity of the wave is
*
1 point
a) 64 cm/s, in - X-direction
(b) 32 cm/s, in - X-direction
(c) 32 cm/s, in + X-direction
(d) 64 cm/s, in + X-direction
95. Displacement between maximum potential energy position and maximum kinetic energy position for a particle executing simple harmonic motion is
*
1 point
(a) ±a/2
(b) +a
(c) ± a
(d) -1
96. A wave travelling along positive x-axis is given by y A = − sin (ωt kx). If it is reflected from rigid boundary such that 80% amplitude is reflected, then equation of reflected wave is
*
1 point
(a) y = A sin (wt + kx)
(b) y = -0.8 A sin (wt + kx)
(c) y = 0.8 A sin (wt + kx)
(d) y = A sin (wt + 0.8 kx)
97. In case of a forced vibration, the resonance peak becomes very sharp when the
*
1 point
(a) damping force is small
(b) restoring force is small
(c) applied periodic force is small
(d) quality factor is small
98. A transverse wave is travelling along a string from left to right. The adjoining figure represents the shape of the string a given instant. At this instant, among the following, choose the wrong statement
*
1 point
(a) Points D, E and F have upwards positive velocity
(b) Points A, B and H have downwards negative velocity
(c) Point C and G have zero velocity
(d) Points A and E have minimum velocity
99. For the wave shown in figure given below, the frequency and wavelength, if its speed is 320 m/s, are
*
1 point
(a) 8 cm, 400 Hz
(b) 80 cm, 40 Hz
(c) 8 cm, 4000 Hz
(d) 40 cm, 8000 Hz
100. The distance between two points differing in phase by 60º on a wave having a wave velocity 360 m/s and frequency 500 Hz is
*
1 point
a) 0.72 metre
(b) 0.18 metre
(c) 0.12 metre
(d) 0.36 metre
101. A simple harmonic wave train of amplitude 2 cm and time period 0.01 sec is travelling with a velocity of 10 m/s in the positive X-direction. The displacement of the particle from the mean position, the particle velocity and particle acceleration at x = 150 cm from the origin and at t = 3 seconds are
*
1 point
(a) 0, 0, 0
(b) 0, 400 p cm/s, 0
(c) 0, 0, 400 p cm/s2
(d) 400 p cm, 0, 0
102. If x a = +t sin ω π 6 and x a ′ = , cosωt then what is the phase difference between the two waves?
*
1 point
(a) π/3
(b) π/6
(c) π/2
(d) π
103. Two particles P and Q describe SHM of same amplitude a, frequency ν along the same straight line. The maximum distance between the two particles is a 2. The initial phase difference between the particles is
*
1 point
(a) zero
(b) π/2
(c) π/6
(d) π/3
104. Three waves of equal frequencies having amplitudes 10mm, 4mm, and 7mm, arrive at a given point with successive phase difference of p/2. The amplitude of the resulting wave (in µ m) is given by
*
1 point
(a) 7
(b) 6
(c) 5
(d) 4
105. A string of length L is stretched by L/20 and the speed of transverse waves along it is v. The speed of wave when it is stretched by L/10 will be (assume that Hooke’s law is applicable)
*
1 point
(a) 2v
(b) v/ √2
(c) √2v
(d) 4v
106. The time period of mass suspended from a spring is T. If the spring is cut into four equal parts and the same mass is suspended from one of the parts, then the new time period will be
*
1 point
(a) T/4
(b) T
(c) T/2
(d) 2T
107. A line source emits a cylindrical wave. If the medium absorbs no energy the amplitude will vary with distance r from the so
*
1 point
(a) r -1
(b) r -2
(c) r -1/2
(d) r1/2
108. A stone thrown into still water, creates a circular wave pattern moving radially outwards. If r is the distance measured from the centre of the pattern, the amplitude of the wave varies as
*
1 point
(a) r-1/2
(b) r-1
(c) r-2
(d) r-3/2
109. Two waves are given by y t 1 = − cos (4 2x) and y t 2 4 2x 4 = − + sin π . The phase difference between the two waves is
*
1 point
(a) π/4
(b) π-/4
(c) 3π/4
(d) π/2
110. The amplitude of a wave is given by A c a b c = ( ) + − Resonance will occur whe
*
1 point
(a) b = -c/2
(b) b = -a/2
(c) b = 0, a = c
(d) None of these
111. The phase difference between two waves, represented by y t 1 x 6 = + 10 100 50 + 0 5 − sin [ ( / ) . ] m y t 2 x 6 = + 10 100 50 − cos[ ( / )] m where x is expressed in metres and t is expressed in seconds, is approximately
*
1 point
(a) 1.07 rad
(b) 2.07 rad
(c) 0.5 rad
(d) 1.5 rad
112. Two waves of frequencies 20 Hz and 30 Hz travel out from a common point. How will they differ in phase at the end of 0.75 second?
*
1 point
(a) 15π
(b) π
(c) 7π
(d) 2π
113. The potential energy of a simple harmonic oscillator when the particle is half way to its end point is
*
1 point
(a) 2/3 E
(b) 1/ 8 E
(c) 1/4 E
(d) 1/2 E
114. Which one of the following statements is true for the speed v and the acceleration a of a particle executing simple harmonic motion?
*
1 point
(a) When v is maximum, a is maximum.
(b) Value of a is zero, whatever may be the value of v.
(c) When v is zero, a is zero.
(d) When v is maximum, a is zero.
115. Pendulum after some time becomes slow in motion and finally stops due to
*
1 point
(a) air friction
(b) earth’s gravity
(c) mass of pendulum
(d) None of theswe
116. Two spring of spring constant k1 and k2 are joined in series. The effective spring constant of the combination is given by
*
1 point
(a) √k1 k2
(b) (k1 + k2)/2
(c) k1 + k2
(d) k1k2/(k1 + k2)
117. A particle executing simple harmonic motion of amplitude 5 cm has maximum speed of 31.4 cm/s. The frequency of its oscillation i
*
1 point
(a) 4 Hz
(b) 3 Hz
(c) 2 Hz
(d) 1 Hz
118. The phase difference between two waves, represented by y t 1 x 6 = + 10 100 50 + 0 5 − sin[ ( / ) . ]m y t 2 x 6 = + 10 100 50 − cos[ ( / )]m, where x is expressed in metres and t is expressed in seconds, is approximately
*
1 point
(a) 1.07 radians
(b) 2.07 radians
(c) 0.5 radian
(d) 1.5 radians
119. When two pendulums X and Y of time period 4 seconds and 4.2 seconds are made to vibrate simultaneously, they are initially in phase. After how many vibrations they will be in the same phase again?
*
1 point
(a) 25
(b) 30
(c) 35
(d) 21
120. The circular motion of a particle with constant speed is
*
1 point
(a) periodic but not simple harmonic.
(b) simple harmonic but not periodic.
(c) periodic and simple harmonic.
(d) neither periodic not simple harmonic.
121. The length of second’s pendulum is 1 m on earth. If mass and diameter of a planet is double than that of earth, then its length on the planet will
*
1 point
(a) 1 m
(b) 2 m
(c) 0.5 m
(d) 4 m
122. A rectangular block of mass m and area of cross-section A floats in a liquid of density r. If it is given a small vertical displacement from equilibrium it undergoes with a time period T, then
*
1 point
(a) T ∝ √1/m
(b) T ∝√ ρ
(c) T ∝ √1/A
(d) T ∝ √1/P
123.. A transverse wave propagating along x-axis is represented by y (x, t) = 8.0 sin (0.5px - 4pt - p/4) where x is in metres and t is in seconds. The speed of the wave is
*
1 point
(a) 8 m/s
(b) 4π m/s
(c) 0.5π m/s
(d)0.5π
124.. A simple pendulum is made of a hollow sphere containing mercury and then suspended by means of a wire. If a little mercury is drained off, the period of pendulum will
*
1 point
(a) remain unchanged
(b) increase
(c) decrease
(d) become erratic
125. The phase difference between the instantaneous velocity and acceleration of a particle executing simple harmonic motion is
*
1 point
(a) π ⋅
(b) 0.707π ⋅
(c) zero
(d) 0 5. π ⋅
126. The particle executing simple harmonic motion has a kinetic energy Ko cos2 wt. The maximum values of the potential energy and the total energy are respectively
*
1 point
(a) K/2 and Ko
(b) Ko and 2Ko
(c) Ko and Ko
(d) 0 and 2K
127 A mass of 2.0 kg is put on a flat pan attached to a vertical spring fixed on the ground as shown in the figure. The mass of the spring and the pan is negligible. When pressed slightly and released the mass executes a simple harmonic motion. The spring constant is 200 N/m. What should be the minimum amplitude of the motion so that the mass gets detached from the pan (take g = 10 m/s2 )
*
1 point
(a) 10.0 cm
(b) any value less than 12.0 cm
(c) 4.0 cm
(d) 8.0 cm
128. A particle executes simple harmonic oscillation with an amplitude a. The period of oscillation is T. The minimum time taken by the particle to travel half of the amplitude from the equilibrium position is
*
1 point
(a) T/8
(b) T/12
(c) T/2
(d) T/4
129. In case of forced vibration, the resonance wave becomes very sharp, when the
*
1 point
(a) applied periodic for is small
(b) quality factor is small
(c) damping force is small
(d) restoring periodic force is small
130. A body executes simple harmonic motion under the action of force F1 with a time period 4/5 seconds. If the force is changed to F2 , it executes simple harmonic motion with a time period 3/5 seconds. If both the forces F1 and F2 act simultaneously in the same direction on the body, its time period will be
*
1 point
(a) 12/25 seconds
(b) 15/12 seconds
(c) 24/25 seconds
(d) 35/24 seconds
131. A block is resting on a piston, which is moving vertically with SHM of period 10 seconds. At what amplitude of motion will the block and piston separate
*
1 point
(a) 0.2 m
(b) 0.25 m
(c) 0.3 m
(d) 0.35 m
132. A spring of force constant k is cut into two pieces, whose lengths are in the ratio 1 : 2. What is the force constant of the longer piece?
*
1 point
(a) k/2
(b) 3k/2
(c) 2k
(d) 3k
133.. The energy of a spring is U (in J), when stretched by 2 cm, the energy (in J) of the spring will be
*
1 point
(a) U
(b) 5U
(c) 25U
(d) 50U
134. The displacement of a particle is represented by the equation y = 3 4 cos 2 π ω The motion of the particle is
*
1 point
(a) simple harmonic with period 2p/w.
(b) simple harmonic with period p/w.
(c) periodic but not simple harmonic.
(d) non-periodic
135. The displacement of a particle is represented by the equation y = sin3 ωt. The motion is
*
1 point
(a) non-periodic.
(b) periodic but not simple harmonic
(c) simple harmonic with period 2p/w.
(d) simple harmonic with period 2p/w
136. The relation between acceleration and displacement of four particles are given below:
*
1 point
(a) ax = +2x.
(b) ax = +2x2,
(c) ax = –2x2.
(d) ax = –2x.
137. Motion of an oscillating liquid column in a U-tube is
*
1 point
(a) periodic but not simple harmonic.
(b) non-periodic.
(c) simple harmonic and time period is independent of the density of the liquid.
(d) simple harmonic and time-period is directly proportional to the density of the liquid
138. A particle is acted simultaneously by mutually perpendicular simple hormonic motions x = a cos wt and y = a sin wt. The trajectory of motion of the particle will be
*
1 point
(a) an ellipse.
(b) a parabola.
(c) a circle.
(d) a straight line.
139. The displacement of a particle varies with time according to the relation y = a sin wt + b cos wt
*
1 point
(a) The motion is oscillatory but not SHM.
(b) The motion is SHM with amplitude a + b.
(c) The motion is SHM with amplitude a2+ b2
(d) The motion is SHM with amplitude a b 2 2
140. Four pendulums A, B, C and D are suspended from the same elastic support as shown in Fig. A and C are of the same length, while B is smaller than A and D is larger than A. If A is given a transverse displacement,
*
1 point
(a) D will vibrate with maximum amplitude.
(b) C will vibrate with maximum amplitude.
(c) B will vibrate with maximum amplitude.
(d) All the four will oscillate with equal amplitude
141. As shown in Fig. shows the circular motion of a particle. The radius of the circle, the period, sense of revolution and the initial position are indicated on the figure. The simple harmonic motion of the x-projection of the radius vector of the rotating particle P is
*
1 point
(a) x (t) = B sin (2π t/30)
(b) x (t) = B cos (π t/15)
(c) x (t) = B sin (π t/15+ π /2)
(d) x (t) = B cos (π t/15+ π /2)
142. The equation of motion of a particle is x = a cos (at)2 . The motion is
*
1 point
(a) periodic but not oscillatory.
(b) periodic and oscillatory.
(c) oscillatory but not periodic.
(d) neither periodic nor oscillatory.
143. A particle executing SHM has a maximum speed of 30 cm/s and a maximum acceleration of 60 cm/s2 . The period of
*
1 point
(a) πs.
(b) ⋅π/2 s.
(c) 2 s.π
(d) ⋅π/t s.
144. When a mass m is connected individually to two springs S1 and S2 , the oscillation frequencies are ν1 and ν2 . If the same mass is attached to the two springs as shown in Fig. The oscillation frequency would be
*
1 point
(a) ν1 + ν2
(b) √ν21 +ν2 2.
(c) (1 /v1+1/v2)-1
(d) √ν21 +ν2 2
145. Water waves produced by a motor boat sailing in water are
*
1 point
(a) neither longitudinal nor transverse.
(b) both longitudinal and transverse.
(c) only longitudinal.
(d) only transverse.
146. Sound waves of wavelength λ travelling in a medium with a speed of v m/s enter into another medium where its speed is 2v m/s. Wavelength of sound waves in the second medium is
*
1 point
(a) λ
(b) 3λ
(c) 2λ
(d) 4λ
147. Speed of sound wave in air
*
1 point
(a) is independent of temperature.
(b) increases with pressure.
(c) increases with increase in humidity.
(d) decreases with increase in humidity.
148 Change in temperature of the medium changes
*
1 point
(a) frequency of sound waves.
(b) amplitude of sound waves.
(c) wavelength of sound waves.
(d) loudness of sound waves.
149. With propagation of longitudinal waves through a medium, the quantity transmitted is
*
1 point
(a) matter.
(b) energy.
(c) energy and matter.
(d) energy, matter and momentum.
150. Which of the following statements are true for wave motion?
*
1 point
(a) Mechanical transverse waves can propagate through all mediums.
(b) Longitudinal waves can propagate through solids only.
(c) Mechanical transverse waves can propagate through solids only.
(d) Longitudinal waves can propagate through vacuum.
151. A sound wave is passing through air column in the form of compression and rarefaction. In consecutive compressions and rarefactions
*
1 point
(a) density remains constant.
(b) Boyle’s law is obeyed.
(c) bulk modulus of air oscillates.
(d) there is no transfer of heat
152. A string of mass 2.5 kg is under a tension of 200 N. The length of the stretched string is 20.0 m. If the transverse jerk is struck at one end of the string, the disturbance will reach the other end in
*
1 point
(a) one second
(b) 0.5 second
(c) 2 seconds
(d) data given is insufficient
153. The composition of two simple harmonic motions of equal periods at right angles to each other and with a phase difference of π, results in the displacement of the particle along a
*
1 point
(a) straight line
(b) circle
(c) hexagon
(d) ellipse
154. The periodic time of a body executing SHM is 4 seconds. After how much interval from time t = 0, its displacement will be half of its amplitude?
*
1 point
(a) 1/4 second
(b) 1 /2 second
(c) 1 /6 second
(d) 1 /3 second
155. If a spring of mass 30 kg has spring constant of 15 N/m, then its time period, is
*
1 point
(a) 2π seconds
(b) 2√ 2π seconds⋅
(c) 2√ 2 seconds
(d) 2 π √2 seconds
156. The equation of a wave is given by: y t = + 10 2 30 sin . π α If the displacement is 5 cm at t = 0, then the total phase at t = 7.5 seconds will be
*
1 point
(a) 2π/3 ⋅ radian
(b) π/3 ⋅ radian
(c) π/2 ⋅ radian
(d) 2π/5 radian
157 A lightly damped oscillator with a frequency (ω) is det in motion by harmonic driving force of frequency (n). When n < ω, then response of the oscillator is controlled by
*
1 point
(a) oscillator frequency
(b) spring constant
(c) damping coefficient
(d) inertia of the mass
158. Time-period of a pendulum on a satellite, orbiting around the earth, is
*
1 point
(a) 0
(b) ∞
(c) 1/π
(d) π
159. If a simple pendulum oscillates with an amplitude of 50 mm and time period of 2 seconds, then its maximum velocity, is
*
1 point
(a) 0.8 m/s
(b) 0.15 m/s
(c) 0.10 m/s
(d) 0.16 m/s
160 The waves in which the particles of the medium vibrate in a direction perpendicular to the direction of wave motion is known as
*
1 point
(a) propagated waves
(b) longitudinal waves
(c) transverse wave
(d) None of these
161. If the period of oscillation of mass M suspended from a spring is 2 seconds, then the period of mass 4M will be
*
1 point
(a) 3T
(b) 2T
(c) T
d) 4T
162 The number of waves, contained in unit length of the medium, is called
*
1 point
(a) wave pulse
(b) wave number
(c) elastic wave
(d) electromagnetic wave
163. If the metal bob of a simple pendulum is replaced by a wooden bob, then its time period will
*
1 point
(a) remain the same
(b) decrease
(c) increase
(d) first (b) then (c
164. A particle executes simple harmonic motion with an angular velocity and maximum acceleration of 3.5 rad/s and 7.5 m/s2 respectively. Amplitude of the oscillation is
*
1 point
(a) 0.36
(b) 0.28
(c) 0.61
(d) 0.53
165. For a particle executing simple harmonic motion, which of the following statements is not correct?
*
1 point
(a) Restoring force is maximum at the extreme positions.
(b) Total energy of the particle always remains the same.
(c) Restoring force is always directed towards a fixed point.
(d) Acceleration of the particle is maximum at the equilibrium position
166. A simple pendulum has a bob suspended by an inextensible thread of length 1 meter rom a point A of suspension. At the extreme position of oscillation, the thread is suddenly caught by a peg at a point B distant (1/4) m from A and the bob begins to oscillate in the new condition. The change in frequency of oscillation of the pendulum is approximately given by (g = 10 m/s2 )
*
1 point
(a) √10/2 HZ
(b) 1/4 √10 HZ
(c) √10/3 HZ
(d) 1√10 HZ
167. The time period of a simple pendulum is T remaining at rest inside a lift. Find the time period of pendulum when lift starts to move up with an acceleration of g/4
*
1 point
(a) T
(b) T/2
(c) 2T/5
(d) 2T /√5
168. From the given figure find the frequency of oscillation of the mass m.
*
1 point
(a) n =1/2π √K/m
(b) n =1/2π √K/2m
(c) n =2π √m/2k
(d) n = 1/2π √m/2k
169. Two springs of force constants k and 2k are connected to a mass as shown in figure. The frequency of oscillation of the mass is
*
1 point
(a) 1/2π √k/m
(b) 1/2π √2k/m
(c) 1/2π √3k/m
(d) 1/2π √m/k
170. The waves produced by a motorboat sailing in water are
*
1 point
(a) transverse
(b) longitudinal
(c) longitudinal and transverse
(d) stationary
171. Two springs are connected to a block of mass M placed on a frictionless surface as shown below. If both the springs have a spring constant k, the frequency of oscillation of the block is
*
1 point
(a) 1/2π √k/M
(b) 1/2 π√ K/2M
(c) 1/2π√2K/M
(d) 1/2π √M/k
172. Which of the following functions represents a simple harmonic oscillation?
*
1 point
(a) sinwt - coswt
(b) sin2 wt
(c) sinwt + sin2wt
(d) sinwt - sin2wt
173. A boat at anchor is rocked by waves whose crests are 100 m apart and velocity is 25 m/s. The boat bounces up once in every
*
1 point
(a) 2500 seconds
(b) 75 seconds
(c) 4 seconds
d) 0.25 second
174. For a wave propagating in a medium, identify the property that is independent of the others.
*
1 point
(a) velocity
(b) wavelength
(c) frequency
(d) all these depend on each other
175. A large horizontal surface moves up and down in SHM with an amplitude of 1 cm. If a mass of 10 kg (which is placed on the surface) is to remain continuously in contact with it, the maximum frequency of SHM will be
*
1 point
(a) 5 Hz
(b) 0.5 Hz
(c) 1.5 Hz
(d) 10 Hz
176 Five sinusoidal waves have the same frequency 500 Hz but their amplitudes are in the ratio 2 1 2 1 2 :::1 1: and their phase angles 0 6 3 2 ,,, πππ ⋅ and π respectively. The phase angle of resultant wave obtained by the superposition of these five waves is
*
1 point
(a) 30°
(b) 45 °
(c) 60°
(d) 90 °
177. Let T1 and T2 be the time periods of springs A and B when mass M is suspended from one end of each spring. If both springs are taken in series and the same mass M is suspended from the series combination, the time period is T, then
*
1 point
(a) T1 + T2 + T3
(b) 1/T= 1/T1+ 1/T2
(c) T2= T2 1+ T 2 1
(d) T2= T2 1+ T 2
178. If maximum speed of a particle in SHM is given by Vm, what is its average speed?
*
1 point
(a) π/2 Vm
(b) 2/π Vm
(c) π/4 Vm
(d) Vm/√2
179. Which of the following equation does not represent a SHM?
*
1 point
(a) coswt + sinwt
(b) sinwt - coswt
(c) 1 - sin2wt
(d) sinwt + cos(wt + α)
180. In simple harmonic motion, loss of kinetic energy is proportional to
*
1 point
(a) ex
(b) x3
(c) logx
(d) x2
181. Two sinusoidal waves of intensity I having same frequency and same amplitude interferes constructively at a point. The resultant intensity at a point will be
*
1 point
(a) I
(b) 2I
(c) 4I
(d) 8I
182 A particle moving about its equilibrium position with equation y = -ax - bt. Interpret the condition
*
1 point
(a) It will always perform the SHM
(b) It can never perform the SHM
(c) It can perform SHM only when t ≥ bx/a
(d) It can perform SHM only when t ≤ ⋅bx/a
183. A simple pendulum performs simple harmonic motion about x = 0 with an amplitude d and time period T. The speed of the pendulum at x = a/2 will be
*
1 point
(a) π a/T
(b) 3 π 2a/T
(c) πa√3/T
(d) π a√3/2T
184. As shown in figure a simple harmonic motion oscillator having identical four strings has time period
*
1 point
(a) T=2π √m/4k
(b) T=2π √m/2k
(b) 2π √m/k
(d) 2π √m/8k
185. The velocity of a particle moving in the x-y plane is given by: dx dt = 8π sin 2pt and dy dt = 5π cos 2pt where, t = 0, the path of the particle is
*
1 point
(a) a straight line
(b) an ellipse
(c) a circle
(d) a parabola
186. The velocity vector v and displacement vector x of a particle executing SHM are related as vdv dx = -w2 x with the initial condition v = vo at x = 0. The velocity v, when displacement is x, is
*
1 point
(a) v= √v2o +ω2 x2
(b) v= √v2o -ω2 x2
(c) v= 3√v3o -ω3 x3
(d) v=vo- (ω3 x3 e x3)1/3
187 Two simple harmonic motions are represented by the equations y1 = 0 1 100 3 . sin π π t + and y2 = 0.1 cospt. The phase difference of the velocity of particle 1 with respect to the velocity of particle 2 is at t = 0
*
1 point
(a) −π/3
(b) π/6
(c) −π/6
(d) π/3
188. A simple pendulum is setup in a trolly which moves to the right with an acceleration a on a horizontal plane. Then, the thread of the pendulum in the mean position makes an angle with the vertical
*
1 point
(a) tan−1 a/g in the forward direction
(b) tan−1 a/g in the backward direction
(c) tan−1 g/a in the backward direction
(d) tan−1 g/a in the backward direction
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