Simple Harmonic Motion PYQs Set 2 (PDF)

Set 2 of 11 · Questions 31-60 of 328

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Mere Teacher · Previous Year Questions NEET Physics · Simple Harmonic Motion · Set 2 (Q31-60)
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31. $A particle is executing a simple harmonic motion. Its maximum acceleration is α and maximum velocity is β. Then its time period of vibration will be:$ (1) $\frac{α}{β}$ (2) $\frac{β ^{2}}{α}$ (3) $\frac{2 πβ}{α}$ (4) $\frac{β ^{2}}{α ^{2}}$ 32. $A body is executing simple harmonic motion with frequency n, the frequency of its potential energy is [NEET 2021]$ (1) $n$ (2) $2 n$ (3) $3 n$ (4) $4 n$ 33. $A mass M, attached to a horizontal spring, executes SHM with a amplitude A_{1} . When the mass M passes through its mean position then a smaller mass m is placed over it and both of them move together with amplitude A_{2} . The ratio of (\frac{A _{1}}{A _{2}}) is:$ (1) $\frac{M}{M + m}$ (2) $\frac{M + m}{M}$ (3) $(\frac{M}{M + m})^{1/2}$ (4) $(\frac{M + m}{M})^{1/2}$ 34. $A particle of mass m oscillates along x ‐axis according to equation x = asinωt . The nature of the graph between momentum and displacement of the particle is$ (1) $Circle$ (2) $Hyperbola$ (3) $Ellipse$ (4) $Straight line passing through origin$ 35. $A point mass oscillates along the x-axis according to the law x = x_{0} cos (ꞷt - π/4). If the acceleration of the particle is written as, a = A cos(ꞷt + δ), then$ (1) $A = x0 , δ = -π/4$ (2) $A = x0ꞷ2, δ = -π/4$ (3) $A = x0ꞷ2, δ = π/4$ (4) $A = x0ꞷ2, δ = 3π/4$ 36. $Two simple harmonic motions of angular frequency 100 and 1000 rad s^{- 1} have the same displacement amplitude. The ratio of their maximum acceleration is$ (1) $1: 1 0^{3}$ (2) $1: 1 0^{4}$ (3) $1: 10$ (4) $1: 1 0^{2}$ 37. $The particle executing simple harmonic motion has a kinetic energy K_{0} co s^{2} o) t . The maximum values of the potential energy and the total energy are respectively$ (1) $K_{0} /2 and K_{0}$ (2) $K_{0} and 2 K_{0}$ (3) $K_{0} and K_{0}$ (4) $0 and 2 K_{0} .$ 38. $A particle is executing SHM along a straight line. Its velocities at distances x_{1} and x_{2} from the mean position are v_{1} and v_{2}, respectively. Its time period is$ (1) $2 π \frac{x _{1}^{2} + x _{2}^{2}}{v _{1}^{2} + v _{2}^{2}}$ (2) $2 π \frac{x _{2}^{2} - x _{1}^{2}}{v _{1}^{2} - v _{2}^{2}}$ (3) $2 π \frac{v _{1}^{2} + v _{2}^{2}}{x _{1}^{2} + x _{2}^{2}}$ (4) $2 π \frac{v _{1}^{2} - v _{2}^{2}}{x _{1}^{2} - x _{2}^{2}}$ 39. $A pendulum has a time period T in air. When it is made to oscillate in water its time period is 2 T . Then the relative density of the material of the bob of the pendulum is (neglect damping)$ (1) $2$ (2) $2$ (3) $22$ (4) $3$ 40. $Consider a simple harmonic motion (SHM). Let K and U be kinetic energy and potential energy when the displacement in SHM is one-half (\frac{1}{2}) the amplitude.Which of the correct statement?$ (1) $\frac{K}{U} = 1$ (2) $\frac{K}{U} = \frac{1}{2}$ (3) $\frac{K}{U} = \frac{4}{3}$ (4) $\frac{K}{U} = 3$ 41. $A rubber ball filled with water, having a small hole is used as the bob of a simple pendulum. The time period of such a pendulum$ (1) $is a constant$ (2) $decreases with time$ (3) $increases with time$ (4) $first increases and then decreases, finally having same value as at the beginning.$ 42. $The circular motion of a particle with constant speed is$ (1) $periodic but not simple harmonic$ (2) $simple harmonic but not periodic$ (3) $period and simple harmonic$ (4) $neither periodic not simple harmonic.$ 43. $A body is executing S.H.M. At a displacement ' x' its potential energy is 9 J and at a displacement ' y' its potential energy is 16 J . The potential energy at displacement (x + y) is$ (1) $25 J$ (2) $5 J$ (3) $49 J$ (4) $7 J$ 44. $The bob of simple pendulum having length l, is displaced from mean position to an angular position 6 with respect to vertical. If it is released, then velocity of bob at equilibrium position$ (1) $2 gl (1 - cos Θ)$ (2) $2 gl (1 + cos Θ)$ (3) $2 gl cos Θ$ (4) $2 gl .$ 45. $The path length of oscillation of a simple pendulum of length 1 meter is 16 cm . Its maximum velocity is (g = π^{2} m / s^{2})$ (1) $2 πcm / s$ (2) $4 πcm / s$ (3) $8 πcm / s$ (4) $16 πcm / s$ 46. $The motion of a simple pendulum excuting S.H.M. is represented by following equation. Y = A sin (πt + φ), where time is measured in second. The length of pendulum is:$ (1) $97.23 cm$ (2) $25.3 cm$ (3) $99.4 cm$ (4) $406.1cm$ 47. $Which of the following functions represents a simple harmonic oscillation?$ (1) $sin ωt - cos ωt$ (2) $sin2 ωt$ (3) $sin ωt + sin 2 ωt$ (4) $sin ωt - sin 2ωt$ 48. $A simple pendulum of length 1 m and having a bob of mass 100 g is suspended in a car, moving on a circular track of radius 100 m with uniform speed 10 m / s . If the pendulum makes small oscillation in a radial direction about its equilibrium position, then its time period can be given by T = 2 π / α^{1/4} . The value of α is [Take g = 10 m / s^{2}]$ (1) $11$ (2) $110$ (3) $101$ (4) $1100$ 49. $A simple pendulum of length L has mass M and it oscillates freely with amplitude A . At extreme position, its potential energy is (g = acceleration due to gravity)$ (1) $\frac{Mg A ^{2}}{2 L}$ (2) $\frac{MgA}{2 L}$ (3) $\frac{Mg A ^{2}}{L}$ (4) $\frac{2 Mg A ^{2}}{L}$ 50. $An object of mass 3 kg is executing simple harmonic motion with an amplitude \frac{2}{π} m . If the kinetic energy of the object when it crosses the mean position is 6 J, the time period of oscillation of the object is$ (1) $1 s$ (2) $2 s$ (3) $3 s$ (4) $4 s$ 51. $A particle is executing simple harmonic motion. If the minimum time taken by the particle to move from extreme position to half of the amplitude is t_{1}, and the minimum time taken by the particle to move from mean position to half of the amplitude is t_{2}, then$ (1) $t_{1} = t_{2}$ (2) $t_{1} = 0.5 t_{2}$ (3) $t_{1} = 2 t_{2}$ (4) $t_{1} = 2 t_{2}$ 52. $A particle executing a simple harmonic motion has a period of 6 sec . The time taken by the particle to move from the mean position to half the amplitude, starting from the mean position is$ (1) $\frac{3}{2} sec$ (2) $\frac{1}{2} sec$ (3) $\frac{3}{4} sec$ (4) $\frac{1}{4} sec$ 53. $Two stars of masses 3 \times 1 0^{31} k g each, and at distance 2 \times 1 0^{11} m rotate in a plane about their common centre of mass O . A meteorite passes through O moving perpendicular to the star's rotation plane. In order to escape from the gravitational field of this double star, the minimum speed that meteorite should have at O is: (Take Gravitational constant G = 6.6 \times 1 0^{- 11} N m^{2} k g^{- 2})$ (1) $2.4 \times 10^{4} m / s$ (2) $1.4 \times 10^{5} m / s$ (3) $3.8 \times 10^{4} m / s$ (4) $2.8 \times 10^{5} m / s$ 54. $The motion of a particle varies with time according to the relation y = a (sin ω t + cos ω t), then$ (1) $The motion is oscillatory but not S.H.M.$ (2) $The motion is S.H.M. with amplitude a$ (3) $The motion is S.H.M. with amplitude a 2$ (4) $The motion is S.H.M. with amplitude 2 a$ 55. $A particle is projected with velocity V_{0} along x - axis. A damping forceis acting on the particle which isproportional to the square of the distance from the origin i.e. ma = - α X^{2} . The distance at which the particle stops:$ (1) $(\frac{2 v _{0}}{3 α})^{\frac{1}{3}}$ (2) $(\frac{3 v _{0}^{2}}{2 α})^{\frac{1}{2}}$ (3) $(\frac{3 v _{0}^{2}}{2 α})^{\frac{1}{3}}$ (4) $(\frac{2 v _{0}^{2}}{3 α})^{\frac{1}{2}}$ 56. $The maximum force acting on a particle executing simple harmonic motion is 10 N . The force on the particle when it is midway between mean and extreme positions will be$ (1) $10 N$ (2) $12 N$ (3) $5 N$ (4) $zero$ 57. $The maximum velocity of a particle performing S.H.M. is 'V?. If the periodic time is made (\frac{1}{3})^{rd} and the amplitude is doubled, then the new maximum velocity of the particle will be$ (1) $\frac{V}{6}$ (2) $3 V 2$ (3) $3 V$ (4) $6 V$ 58. $A spring is stretched by 5 cm by a force 10 N. The time period of the oscillations when a mass of 2 kg is suspended by it is [NEET 2021]$ (1) $0.0628 s$ (2) $6.28 s$ (3) $3.14 s$ (4) $0.628 s$ 59. $A body starting at t = 0 from origin and oscillates simple harmonically with a period of 4 s . After what time will its kinetic energy by 75 % of its total energy.$ (1) $1/2 s$ (2) $1/3. s$ (3) $1/4 s$ (4) $1 s .$ 60. $A particle performs simple harmonic motion at a frequency f. The frequency at which its kinetic energy varies is$ (1) $f$ (2) $2f$ (3) $4f$ (4) $\frac{f}{2}$