Question

A block of mass $m$ is resting on a piston as shown in the figure which is moving vertically in a SHM of period $1s.$ The minimum amplitude of motion at which the block and piston separate is :

• A. $0.25m$
• B. $0.52m$
• C. $2.5m$
• D. $0.15m$

Answer 1

The correct option is A $0.25m$

T = time period 1 s

Angular frequency $\omega =\frac{2\pi }{T}=2\pi$ rad/s

Equation of motion of block

N-mg = ma $|$ a= acceleration of S.H.M $|$

Now at extreme position

$a=-{\omega }^{2}A$ |A = amplitude of S.H.M.|

separation will begin when N = 0 i.e, (a=g)

$a=-{\omega }^{2}A=g$

$\Rightarrow A=\frac{g}{{\omega }^2}=\frac{10}{4{\pi }^2}\approx \frac{10}{4\times 10}\Rightarrow A=0.26m$ (separation occur at extreme position with amplitude 0.25m)