Question

A flat horizontal board moves up and down under S.H.M. vertically with amplitude $A$. The shortest permissible time period of the vibration such that an object placed on the board may not lose contact with the board is

• A. $2 \pi \sqrt{\frac{g}{A}}$
• B. $2 \pi \sqrt{\frac{A}{g}}$
• C. $2 \pi \sqrt{\frac{2 A}{g}}$
• D. $\frac{\pi}{2} \sqrt{\frac{A}{g}}$

Answer 1

Answer: (B)

Maximum acceleration of the system $\left(a_{\max }\right)=-\omega^{2} A$
For a block to escape the board the acceleration must be equal to $9$ at the top-most point.
$g=\omega^{2} A$
$\omega=\sqrt{\frac{g}{A}}$
Time period $=\frac{2 \pi}{\omega}=\sqrt{\frac{A}{g}}$