Simple Harmonic Motion PYQs Set 3 (PDF)

Set 3 of 13 · Questions 61-90 of 372

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Mere Teacher · Previous Year Questions JEE Main Physics · Simple Harmonic Motion · Set 3 (Q61-90)
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61. $An object of mass 3 kg is executing simple harmonic motion with an amplitude \frac{2}{π} m . If the kinetic energy of the object when it crosses the mean position is 6 J, the time period of oscillation of the object is$ (1) $1 s$ (2) $2 s$ (3) $3 s$ (4) $4 s$ 62. $A particle is executing simple harmonic motion. If the minimum time taken by the particle to move from extreme position to half of the amplitude is t_{1}, and the minimum time taken by the particle to move from mean position to half of the amplitude is t_{2}, then$ (1) $t_{1} = t_{2}$ (2) $t_{1} = 0.5 t_{2}$ (3) $t_{1} = 2 t_{2}$ (4) $t_{1} = 2 t_{2}$ 63. $A particle executing a simple harmonic motion has a period of 6 sec . The time taken by the particle to move from the mean position to half the amplitude, starting from the mean position is$ (1) $\frac{3}{2} sec$ (2) $\frac{1}{2} sec$ (3) $\frac{3}{4} sec$ (4) $\frac{1}{4} sec$ 64. $Two stars of masses 3 \times 1 0^{31} k g each, and at distance 2 \times 1 0^{11} m rotate in a plane about their common centre of mass O . A meteorite passes through O moving perpendicular to the star's rotation plane. In order to escape from the gravitational field of this double star, the minimum speed that meteorite should have at O is: (Take Gravitational constant G = 6.6 \times 1 0^{- 11} N m^{2} k g^{- 2})$ (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) $2.8 \times 10^{5} m / s$ 65. $The motion of a particle varies with time according to the relation y = a (sin ω t + cos ω t), then$ (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) $The motion is S.H.M. with amplitude 2 a$ 66. $A particle is projected with velocity V_{0} along x - axis. A damping forceis acting on the particle which isproportional to the square of the distance from the origin i.e. ma = - α X^{2} . The distance at which the particle stops:$ (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) $(\frac{2 v _{0}^{2}}{3 α})^{\frac{1}{2}}$ 67. $The maximum force acting on a particle executing simple harmonic motion is 10 N . The force on the particle when it is midway between mean and extreme positions will be$ (1) $10 N$ (2) $12 N$ (3) $5 N$ (4) $zero$ 68. $The maximum velocity of a particle performing S.H.M. is 'V?. If the periodic time is made (\frac{1}{3})^{rd} and the amplitude is doubled, then the new maximum velocity of the particle will be$ (1) $\frac{V}{6}$ (2) $3 V 2$ (3) $3 V$ (4) $6 V$ 69. $A spring is stretched by 5 cm by a force 10 N. The time period of the oscillations when a mass of 2 kg is suspended by it is [NEET 2021]$ (1) $0.0628 s$ (2) $6.28 s$ (3) $3.14 s$ (4) $0.628 s$ 70. $A body starting at t = 0 from origin and oscillates simple harmonically with a period of 4 s . After what time will its kinetic energy by 75 % of its total energy.$ (1) $1/2 s$ (2) $1/3. s$ (3) $1/4 s$ (4) $1 s .$ 71. $A particle performs simple harmonic motion at a frequency f. The frequency at which its kinetic energy varies is$ (1) $f$ (2) $2f$ (3) $4f$ (4) $\frac{f}{2}$ 72. $A particle executes S.H.M., the graph of velocity as a function of displacement is:$ (1) $a circle$ (2) $a parabola$ (3) $an ellipse$ (4) $a helix$ 73. $T_{0} is the time period of a simple pendulum at a place. If the length of the pendulum is reduced to \frac{1}{16} times of its initial value, the modified time period is:$ (1) $T_{0}$ (2) $8 π T_{0}$ (3) $4 T_{0}$ (4) $\frac{1}{4} T_{0}$ 74. $Choose the correct length (L) versus square of time period (T^{2}) graph for a simple pendulum executing simple harmonic motion.$ (1) (2) (3) (4) 75. $The equation of motion of a particle executing simple harmonic motion is 4 \frac{d ^{2} y}{dt ^{2}} + π^{2} y = 0 where y is in metres and t is in seconds. The time period of oscillation, the particle is$ (1) $1 s$ (2) $2 s$ (3) $3 s$ (4) $4 s$ 76. $Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): Knowing initial position x0 and initial momentum p0 is enough to determine the position and momentum at any time t for a simple harmonic motion with a given angular frequency ω. Reason (R): The amplitude and phase can be expressed in terms of x0 and p0. choose the correct answer from the options given below:$ (1) $(A) is false but (R) is true$ (2) $(A) is true but (R) is false$ (3) $Both (A) and (R) are true but (R) is NOT the correct explanation of (A)$ (4) $Both (A) and (R) are true and (R) is the correct explanation of (A)$ 77. $A rectangular block of mass ' M' and cross-sectional area ' A' floats on a liquid of density ' ρ'. It is given a small vertical displacement from equilibrium, it starts oscillating with frequency ' n' then$ (1) $n \propto A$ (2) $n \propto A^{2}$ (3) $n \propto A$ (4) $n \propto A^{3}$ 78. $A simple pendulum of length L carries a bob of mass m . When the bob is at its lowest position, it is given that the minimum horizontal speed necessary for it to move in a vertical circle about the point of suspension. When the string is horizontal, the net force on the bob is$ (1) $10 mg$ (2) $5 mg$ (3) $4 mg$ (4) $1 mg$ 79. $The kinetic energy of a simple harmonic oscillator is oscillating with angular frequency of 176rad/s. The frequency of this simple harmonic oscillator is____Hz. [ take π = \frac{22}{7}]$ (1) $14$ (2) $28$ (3) $176$ (4) $88$ 80. $The measured value of the length of a simple pendulum is 20 cm with 2 mm accuracy. The time for 50 oscillations was measured to be 40 seconds with 1 second resolution. From these measurements, the accuracy in the measurement of acceleration due to gravity is N % . The value of N is:$ (1) $4$ (2) $8$ (3) $6$ (4) $5$ 81. $The bob of a simple pendulum performs S.H.M. with period T in air and with period T_{1} in water. Relation between T and T_{1} is (neglect friction due to water, density of the material of the bob = \frac{9}{8} \times 10^{3} kg / m^{3}, density of water 1 g / cc)$ (1) $T_{1} = 3 T$ (2) $T_{1} = 2 T$ (3) $T_{1} = T$ (4) $T_{1} = T 2$ 82. $The displacement of a particle in simple harmonic motion (SHM) is given by y = 3 π sin (\frac{100}{π} t + \frac{π}{4}) . What will be the displacement of the particle from the mean position, when its kinetic energy is eight times that of its potential energy?$ (1) $\frac{π}{3} .$ (2) $\frac{3 π}{2}$ (3) $π$ (4) $3 π$ 83. $A sliver atom in a solid oscillates in simple harmonic motion in some direction with a frequency of 1 0^{12} /sec. What is the force constant of the bonds connecting one atom with the other? (Mole wt. of siver =108 and Avagadro number = 6.02 \times 1 0^{23} gm m o l e^{-1})$ (1) $2.2 N/m$ (2) $5.5 N/m$ (3) $6.4 N/m$ (4) $7.1 N/m$ 84. $A particle executing simple harmonic motion along a straight line with an amplitude A, attains maximum potential energy when its displacement from mean position equals$ (1) $0$ (2) $\pm \frac{A}{2}$ (3) $\pm A$ (4) $\pm \frac{A}{2}$ 85. $The length of a seconds pendulum at a height h = 2R from earth surface will be: (Given: R=Radius of earth and acceleration due to gravity at the surface of earth g = π^{2} m/ s^{- 2})$ (1) $\frac{2}{9} m$ (2) $\frac{4}{9} m$ (3) $\frac{8}{9} m$ (4) $\frac{1}{9} m$ 86. $The angular velocity and the amplitude of a simple pendulum is ω and a respectively. At a displacement x from the mean position if its kinetic energy is T and potential energy is V, then the ratio of T to V is$ (1) $\frac{( a ^{2} - X ^{2} ω ^{2} )}{X ^{2} ω ^{2}}$ (2) $\frac{x ^{2} ω ^{2}}{( a ^{2} - x ^{2} ω ^{2} )}$ (3) $\frac{( a ^{2} - x ^{2} )}{x ^{2}}$ (4) $\frac{x ^{2}}{( a ^{2} - x ^{2} )}$ 87. $The general displacement of a simple harmonic oscillator is x-Asin ω t. Let T be its time period. The slope of its potential energy (U) - time (t) curve will be maximum when t = \frac{T}{β}, The value of β is$ 88. $A particle executes simple harmonic motion with an amplitude of 4 cm . At the mean position, velocity of the particle is 10 cm / s . The distance of the particle from the mean position when its speed becomes 5 cm / s is α cm, where α =______$ 89. $The amplitude of a particle executing SHM is 3 cm. The displacement at which its kinetic energy will be 25% more than the potential energy is: ------------cm,$ 90. $A mass m is suspended from a spring of negligible mass and the system oscillates with a frequency f_{1} . The frequency of oscillations if a mass 9 m is suspended from the same spring is f_{2} . The value of \frac{f _{1}}{f _{2}} is_____$