question_answer

A block is resting on a piston which is moving vertically with SHM of period\[1s\]. At what amplitude of motion will the block and piston separate?

A) \[0.2m\]             

B) \[0.25m\]

C) \[0.3\text{ }m\]               

D) \[0.35m\]

Correct Answer: B

Solution :

When maximum force just exceeds the weight of the body, then weight kept on the system will separate from the piston \[\therefore \]  \[mg=m{{\omega }^{2}}y\] \[\Rightarrow \]                  \[y=\frac{g}{{{\omega }^{2}}}\] Given\[g=9.8\,\,m{{s}^{-2}},\,\,\omega =2\pi \] \[\therefore \]  \[y=\frac{9.8}{{{(2\pi )}^{2}}}=0.25m\]