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MHT CET 2023 (14 May, Shift 2) · Velocity & Acceleration in SHM

Velocity & Acceleration in SHM question from MHT CET 2023 (14 May, Shift 2)

Q46MHT CET 2023 · 14 MAY · SHIFT 2Medium

Velocity & Acceleration in SHM

A block of mass ' $M$ ' rests on a piston executing S.H.M. of period one second. The amplitude of oscillations, so that the mass is separated from the piston, is (acceleration due to gravity, $g = 10\text{ m s}^{-2},\ \pi^2 = 10$ )

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Answer: (a)

The block separates at the top when $\omega^2 A = g$ .
$\omega = \dfrac{2\pi}{T} = 2\pi\text{ rad/s} \Rightarrow \omega^2 = 4\pi^2 = 40$
$A = \dfrac{g}{\omega^2} = \dfrac{10}{40} = 0.25\text{ m}$
So the answer is (a) 0.25 m.

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