Simple Harmonic Motion PYQs Set 2 (PDF)

Set 2 of 13 · Questions 31-60 of 372

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Mere Teacher · Previous Year Questions JEE Main Physics · Simple Harmonic Motion · Set 2 (Q31-60)
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31. $For a simple pendulum, a graph is plotted between its kinetic energy (KE) and potential energy (PE) against its displacement d. Which one of the following represents these correctly? (graphs are schematic and not drawn to scale)$ (1) (2) (3) (4) 32. $Two springs of force constants k_{1} and k_{2} are loaded with weights w_{1} and w_{2} respectively. Assume that, length of each string is increased by same amount. If k_{1} = 2 k_{2}, then the ratio w_{2} / w_{1} is$ (1) $1$ (2) $0.5$ (3) $0.25$ (4) $4$ 33. $Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): A simple pendulum is taken to a planet of mass and radius, 4 times and 2 times, respectively, than the Earth. The time period of the pendulum remains same on earth and the planet. Reason (R): The mass of the pendulum remains unchanged at Earth and the other planet. choose the correct answer from the options given below:$ (1) $(A) is false but (R) is true$ (2) $(A) is true but (R) is false$ (3) $Both (A) and (R) are true and (R) is the correct explanation of (A)$ (4) $Both (A) and (R) are true but (R) is NOT the correct explanation of (A)$ 34. $Two particles A and B of equal masses are suspended from two massless springs of spring constants K_{1} and K_{2} respectively. If the maximum velocities during oscillations are equal, the ratio of the amplitude of A and B is$ (1) $\frac{K _{2}}{K _{1}}$ (2) $\frac{K _{1}}{K _{2}}$ (3) $\frac{K _{1}}{K _{2}}$ (4) $\frac{K _{2}}{K _{1}}$ 35. $The displacement of a particle executing simple harmonic motion is given by y = A_{0} + Asi n ωt + Bco s ωt Then, the amplitude of its oscillation is given by [NEET 2019]$ (1) $A^{2} + B^{2}$ (2) $A02+(A + B)2$ (3) $A + B$ (4) $A_{0} + A^{2} + B^{2}$ 36. $A particle is executing a simple harmonic motion. Its maximum acceleration is α and maximum velocity is β. Then its time period of vibration will be:$ (1) $\frac{α}{β}$ (2) $\frac{β ^{2}}{α}$ (3) $\frac{2 πβ}{α}$ (4) $\frac{β ^{2}}{α ^{2}}$ 37. $A body is executing simple harmonic motion with frequency n, the frequency of its potential energy is [NEET 2021]$ (1) $n$ (2) $2 n$ (3) $3 n$ (4) $4 n$ 38. $A mass M, attached to a horizontal spring, executes SHM with a amplitude A_{1} . When the mass M passes through its mean position then a smaller mass m is placed over it and both of them move together with amplitude A_{2} . The ratio of (\frac{A _{1}}{A _{2}}) is:$ (1) $\frac{M}{M + m}$ (2) $\frac{M + m}{M}$ (3) $(\frac{M}{M + m})^{1/2}$ (4) $(\frac{M + m}{M})^{1/2}$ 39. $A particle of mass m oscillates along x ‐axis according to equation x = asinωt . The nature of the graph between momentum and displacement of the particle is$ (1) $Circle$ (2) $Hyperbola$ (3) $Ellipse$ (4) $Straight line passing through origin$ 40. $A point mass oscillates along the x-axis according to the law x = x_{0} cos (ꞷt - π/4). If the acceleration of the particle is written as, a = A cos(ꞷt + δ), then$ (1) $A = x0 , δ = -π/4$ (2) $A = x0ꞷ2, δ = -π/4$ (3) $A = x0ꞷ2, δ = π/4$ (4) $A = x0ꞷ2, δ = 3π/4$ 41. $Two simple harmonic motions of angular frequency 100 and 1000 rad s^{- 1} have the same displacement amplitude. The ratio of their maximum acceleration is$ (1) $1: 1 0^{3}$ (2) $1: 1 0^{4}$ (3) $1: 10$ (4) $1: 1 0^{2}$ 42. $The particle executing simple harmonic motion has a kinetic energy K_{0} co s^{2} o) t . The maximum values of the potential energy and the total energy are respectively$ (1) $K_{0} /2 and K_{0}$ (2) $K_{0} and 2 K_{0}$ (3) $K_{0} and K_{0}$ (4) $0 and 2 K_{0} .$ 43. $A particle is executing SHM along a straight line. Its velocities at distances x_{1} and x_{2} from the mean position are v_{1} and v_{2}, respectively. Its time period is$ (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) $2 π \frac{v _{1}^{2} - v _{2}^{2}}{x _{1}^{2} - x _{2}^{2}}$ 44. $A pendulum has a time period T in air. When it is made to oscillate in water its time period is 2 T . Then the relative density of the material of the bob of the pendulum is (neglect damping)$ (1) $2$ (2) $2$ (3) $22$ (4) $3$ 45. $Consider a simple harmonic motion (SHM). Let K and U be kinetic energy and potential energy when the displacement in SHM is one-half (\frac{1}{2}) the amplitude.Which of the correct statement?$ (1) $\frac{K}{U} = 1$ (2) $\frac{K}{U} = \frac{1}{2}$ (3) $\frac{K}{U} = \frac{4}{3}$ (4) $\frac{K}{U} = 3$ 46. $A rubber ball filled with water, having a small hole is used as the bob of a simple pendulum. The time period of such a pendulum$ (1) $is a constant$ (2) $decreases with time$ (3) $increases with time$ (4) $first increases and then decreases, finally having same value as at the beginning.$ 47. $The circular motion of a particle with constant speed is$ (1) $periodic but not simple harmonic$ (2) $simple harmonic but not periodic$ (3) $period and simple harmonic$ (4) $neither periodic not simple harmonic.$ 48. $A body is executing S.H.M. At a displacement ' x' its potential energy is 9 J and at a displacement ' y' its potential energy is 16 J . The potential energy at displacement (x + y) is$ (1) $25 J$ (2) $5 J$ (3) $49 J$ (4) $7 J$ 49. $The bob of simple pendulum having length l, is displaced from mean position to an angular position 6 with respect to vertical. If it is released, then velocity of bob at equilibrium position$ (1) $2 gl (1 - cos Θ)$ (2) $2 gl (1 + cos Θ)$ (3) $2 gl cos Θ$ (4) $2 gl .$ 50. $The path length of oscillation of a simple pendulum of length 1 meter is 16 cm . Its maximum velocity is (g = π^{2} m / s^{2})$ (1) $2 πcm / s$ (2) $4 πcm / s$ (3) $8 πcm / s$ (4) $16 πcm / s$ 51. $The motion of a simple pendulum excuting S.H.M. is represented by following equation. Y = A sin (πt + φ), where time is measured in second. The length of pendulum is:$ (1) $97.23 cm$ (2) $25.3 cm$ (3) $99.4 cm$ (4) $406.1cm$ 52. $Which of the following functions represents a simple harmonic oscillation?$ (1) $sin ωt - cos ωt$ (2) $sin2 ωt$ (3) $sin ωt + sin 2 ωt$ (4) $sin ωt - sin 2ωt$ 53. $A simple pendulum of length 1 m and having a bob of mass 100 g is suspended in a car, moving on a circular track of radius 100 m with uniform speed 10 m / s . If the pendulum makes small oscillation in a radial direction about its equilibrium position, then its time period can be given by T = 2 π / α^{1/4} . The value of α is [Take g = 10 m / s^{2}]$ (1) $11$ (2) $110$ (3) $101$ (4) $1100$ 54. $A simple pendulum of length L has mass M and it oscillates freely with amplitude A . At extreme position, its potential energy is (g = acceleration due to gravity)$ (1) $\frac{Mg A ^{2}}{2 L}$ (2) $\frac{MgA}{2 L}$ (3) $\frac{Mg A ^{2}}{L}$ (4) $\frac{2 Mg A ^{2}}{L}$ 55. $A body is performing simple harmonic with an amplitude of 10 cm. The velocity of the body was tripled by air Jet when it is at 5 cm from its mean position. The new amplitude of vibration is x cm. The value of x is__________.$ 56. $A simple pendulum is placed at a place where its distance from the earth's surface is equal to the radius of the earth. If the length of the string is 4 m, then the time period of small oscillations will be ______s. [ take (g = π^{2} ms^{- 2})$ 57. $A mass m attached to free end of a spring executes SHJV t with a period of Is. If the mass is increased by 3 kg the period of oscillation increases by one second, the value of mass m is________kg.$ 58. $An object of mass 0.2 kg executes simple harmonic motion along x axis with frequency of (\frac{25}{π}) Hz . At the position x = 0.04 m the object has kinetic energy 0.5 J and potential energy 0.4 J . The amplitude of oscillation is_____cm .$ 59. $The position, velocity and acceleration of a particle executing simple harmonic motion are found to have magnitudes of 4 m, 2 ms^{- 1} and 16 ms^{- 2} at a certain instant. The amplitude of the motion is x, m where x is____$ 60. $A particle performs simple harmonic motion with amplitude A. Its speed is increased to three times at an instant when its displacement is \frac{2 A}{3} . The new amplitude of motion is \frac{nA}{3} . The value of n is______$