Simple Harmonic Motion PYQs Set 6 (PDF)

Set 6 of 13 · Questions 151-180 of 372

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Mere Teacher · Previous Year Questions JEE Main Physics · Simple Harmonic Motion · Set 6 (Q151-180)
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151. $The ratio of frequencies of two oscillating pendulums are 3 : 2 . Their lengths are in the ratio$ (1) $3 : 2$ (2) $9 : 4$ (3) $4 : 9$ (4) $2 : 3$ 152. $A particle rests in equilibrium under two forces of repulsion whose centers are at distance of a and b from the particle. The forces vary as the cube of the distance. The forces per unit mass are k and k' respectively. If the particle be slightly displaced towards one of them the motion is simple harmonic with the time period equal to$ (1) $\frac{2 π}{3 ( \frac{k}{a ^{3}} + \frac{k ’}{b ^{3}} )}$ (2) $\frac{2 π}{( \frac{k}{a ^{3}} + \frac{k ’}{b ^{3}} )}$ (3) $\frac{2 π}{( \frac{k}{a ^{4}} + \frac{k ’}{b ^{4}} )}$ (4) $\frac{2 π}{3 ( \frac{k}{a} + \frac{k ’}{b} )}$ 153. $Given below are two statements: Statement (I):- A second's pendulum has a time period of 1 second. Statement (II):- It takes precisely one second to move between the two extreme positions. In the light of the above statements, choose the correct answer from the options give below.$ (1) $Both Statement I and Statement II are false$ (2) $Statement I is true but Statement II is false$ (3) $Statement I is false but Statement II is true$ (4) $Both Statement I and Statement II is true$ 154. $A particle is executing a simple harmonic motion. Its maximum acceleration is α and maximum velocity is β . Then, its time period of vibration will be$ (1) $\frac{β ^{2}}{α ^{2}}$ (2) $\frac{α}{β}$ (3) $\frac{β ^{2}}{α}$ (4) $\frac{2 πβ}{α}$ 155. $A particle moves along the X-axis according to the equation x = 10 s i n^{3} (πt). The amplitudes and frequencies of component SHMs are$ (1) $amplitude 30/4, 10/4 ; frequencies 3/2, ½$ (2) $amplitude 30/4, 10/4 ; frequencies 1/2, 3/2$ (3) $amplitude 10, 10 ; frequencies 1/2, ½$ (4) $amplitude 30/4, 10 ; frequencies 3/2, 2$ 156. $For a periodic motion represented by the equation y = sin ω t + cos ω t the amplitude of the motion is$ (1) $1$ (2) $0.5$ (3) $2$ (4) $2$ 157. $particle performing S.H.M. starts from equilibrium position and its time period is 16 second. After 2 seconds its velocity is πm / s . Amplitude of oscillation is (cos 45^{\circ} = \frac{1}{2})$ (1) $22 m$ (2) $42 m$ (3) $62 m$ (4) $82 m$ 158. $A particle moves with simple harmonic motion in a straight line. In first τ s, after starting from rest it travels a distance a, and in next τ s it travels 2a, in same direction, then:$ (1) $amplitude of motion is 3a$ (2) $time period of oscillations is 8τ$ (3) $amplitude of motion is 4a$ (4) $time period of oscillations is 6τ$ 159. $A spring of force constant k is cut into lengths of ratio 1:2: 3. They are connected in series and the new force constant is k^{’} . Then they are connected in parallel and force constant is k Then k^{’} : k^{″} is$ (1) $1:9$ (2) $1: 11$ (3) $1:14$ (4) $1:6$ 160. $A particle of mass 0.1 kg is executing simple harmonic motion of amplitude 0.1 m . When the particle passes through the mean position, its kinetic energy is 8 \times 10^{- 3} J . If the initial phase is 45^{\circ}, the equation of its motion is (Assume, x (t) as the position of the particle at time t .)$ (1) $x (t) = 0.1 sin (4 t + \frac{π}{4})$ (2) $x (t) = 0.1 sin (16 t + \frac{π}{4})$ (3) $x (t) = 0.1 sin (2 (t + \frac{π}{4}))$ (4) $x (t) = 0.1 sin (2 t + \frac{π}{4})$ 161. $Two bar magnets oscillate in a horizontal plane in earth's magnetic field with time periods of 3 s and 4 s respectively. If their moments of inertia are in the ratio of 3 : 2 then the ratio of their magnetic moments will be:$ (1) $2:1$ (2) $8:3$ (3) $1 : 3$ (4) $27 : 1$ 162. $A particle executing SHM has maximum speed of 0.5 m s^{- 1} and maximum acceleration of 1.0 m s^{- 2} . The angular frequency of oscillation is$ (1) $2 rad s^{- 1}$ (2) $0.5 rad s^{- 1}$ (3) $2 πrad s^{- 1}$ (4) $0.5 πrad s^{- 1}$ 163. $Under the action of a force F = - 75 y where F is in Newton and y is in meters, an object of mass 3 kg executes simple harmonic motion. If the velocity of the object at the mean position is 2.5 ms^{- 1}, the maximum acceleration of the object is$ (1) $5 ms^{- 2}$ (2) $7.5 ms^{- 2}$ (3) $10 ms^{- 2}$ (4) $12.5 ms^{- 2}$ 164. $The phase difference between displacement and acceleration of a particle in a simple harmonic motion is [NEET 2020]$ (1) $\frac{3 π}{2} rad$ (2) $\frac{π}{2} rad$ (3) $zero$ (4) $πrad$ 165. $The transverse displacement of a string of a linear density 0.01 kg m^{- 1}, clamped at its ends is given by Y_{(x, t)} = 0.03 sin (\frac{2 πx}{3}) cos (60 πt), where x and y are in metres and time t is in seconds. Tension in the string is$ (1) $9 N$ (2) $36 N$ (3) $162 N$ (4) $81 N$ 166. $If a simple pendulum has significant amplitude (up to a factor of 1/e of original) only in the period between t = 0s to t = τs, then τ may be called the average life of the pendulum. When the spherical bob of the pendulum suffers a retardation (due to viscous drag) proportional to its velocity, with 'b' as the constant of proportionality, the average life time of the pendulum is (assuming damping is small) in seconds:$ (1) $\frac{0.693}{b}$ (2) $b$ (3) $\frac{1}{b}$ (4) $\frac{2}{b}$ 167. $Two particles execute simple harmonic motion along the same straight line with same amplitude and 'same frequency. The two particles pass one another when moving in opposite directions each time at a distance of \frac{1}{2} times the amplitude from their common mean position. The phase difference between the two particles is$ (1) $30^{\circ}$ (2) $45^{\circ}$ (3) $60^{\circ}$ (4) $90^{\circ}$ 168. $A second’s pendulum is mounted in a rocket. Its period of oscillation will decrease when rocket is$ (1) $moving down with uniform acceleration$ (2) $moving around the earth in geostationary orbit$ (3) $moving up with uniform velocity$ (4) $moving up with uniform acceleration.$ 169. $A spring of force constant k is cut into lengths of ratio 1 : 2 : 3 . They are connected in series and the new force constant is k^{’} . If they are connected in parallel and force constant is k^{’ ’}, then k^{’} : k^{’ ’} is [NEET 2017]$ (1) $1 : 6$ (2) $1 : 9$ (3) $1 : 11$ (4) $1 : 14$ 170. $A simple harmonic oscillator of frequency 1 Hz has a phase of 1 rad . By how much should the origin be shifted in time, so as to make the phase of the oscillator vanish? [Time in seconds (s)].$ (1) $- \frac{1}{π} s$ (2) $- \frac{1}{2 π} s$ (3) $- \frac{π}{2} s$ (4) $- πs$ 171. $For a body executing S.H.M.: (A) Potential energy is always equal to its K.E. (B) Average potential and kinetic energy over any given time interval are always equal. (C) Sum of the kinetic and potential energy at any point of time is constant. (D) Average K.E. in one time period is equal to average potential energy in one time period. Choose the most appropriate option from the options given below:$ (1) $(C) and (D)$ (2) $only (C)$ (3) $(B) and (C)$ (4) $only (B)$ 172. $Two simple harmonic motions are represented by y_{1} = 5 [sin 2 πt + 3 cos 2 πt] and y_{2} = 5 sin (2 πt + \frac{π}{4}) . The ratio of their amplitudes is$ (1) $1 : 1$ (2) $2 : 1$ (3) $1 : 3$ (4) $3 : 1$ 173. $A second pendulum is placed in a space laboratory orbiting round the earth at a height ' 3 R' from the earth's surface. The time period of the pendulum will be (R = radius of earth)$ (1) $zero$ (2) $\frac{2}{3} s$ (3) $4 s$ (4) $infinite.$ 174. $Two S.H.Ms are represented by equations y_{1} = 0.1 sin (100 πt + \frac{π}{3}) and y_{2} = 0.1 co s (100 πt) The phase difference between the speeds of the two particles is$ (1) $\frac{π}{3}$ (2) $- \frac{π}{6}$ (3) $+ \frac{π}{6}$ (4) $- \frac{π}{3}$ 175. $A S.H.M. is represents by x = 52 (sin 2πt + cos 2πt). The amplitude of the S.H.M. is:$ (1) $10 cm$ (2) $20 cm$ (3) $52 cm$ (4) $50 cm$ 176. $In a simple harmonic oscillation, what fraction of total mechanical energy is in the form of kinetic energy, when the particle is midway between mean and extreme position.$ (1) $\frac{1}{2}$ (2) $\frac{3}{4}$ (3) $\frac{1}{3}$ (4) $\frac{1}{4}$ 177. $A particle performs simple harmonic motion with amplitude A. Its speed is trebled at the instant that it is at distance \frac{2 A}{3} from equilibrium position. The new amplitude of the motion is.$ (1) $3A$ (2) $A 3$ (3) $\frac{7 A}{3}$ (4) $\frac{A}{3} 41$ 178. $A point mass oscillates along x -axis according to x = x_{0} sin (ωt - \frac{π}{6}) . If the acceleration of the point mass is written as a = Asin (ωt + δ) then$ (1) $A = x_{0}, δ = - \frac{π}{6}$ (2) $A = x_{o} ω^{2}, δ = - \frac{π}{6}$ (3) $A = x_{o} ω^{2}, δ = \frac{π}{6}$ (4) $A = x_{o} ω^{2}, δ = \frac{5 π}{6}$ 179. $A particle excutes S.H.M with amplitude 'a' and time period T . The displacement of the particle when itsspeed is half of maximum speed is \frac{x a}{2} . The value of x is$ 180. $A particle of mass 0.50 kg executes simple harmonic motion under force F = - 50 (Nm^{- 1}) x . The time period of oscillation is \frac{x}{35} s . The value of x is ____ (Given π = \frac{22}{7})$