Question

A block rides on a piston that is moving vertically with simple hormonic motion. The maximum speed of the piston is $2\text{m/s}$. If maxmium acceleration of block during its motion is$a=10{\text{m/s}}^2$, then the amplitude of motion at which the block and piston separates is

• A. $20\text{cm}$
• B. $30\text{cm}$
• C. $40\text{cm}$
• D. $50\text{cm}$

Answer 1

The correct option is C $40\text{cm}$

Given,
$v_{\text{max}}=2\text{m/s}$
We know that, $v_{\text{max}}=A\omega$
$\therefore A\omega =2\text{m/s}$ ... (1)
Since, $a_{\text{max}}={\omega }^{2}A=10\text{m/s}$ ... (2)
From (1) and (2)
$\frac{(v_{\text{max}}{)}^2}{a_{\text{max}}}=A=0.4\text{m}$ or $40\text{cm}$