Question

A plank with a small block on top of it is undergoing vertical SHM. Its period is 2 sec.The minimum amplitude at which the block will separate from plank is :

• A. $\frac{10}{{\pi }^2}$
• B. $\frac{{\pi }^2}{10}$
• C. $\frac{20}{{\pi }^2}$
• D. $\frac{\pi }{10}$

Answer 1

Answer: (A)

$\frac{10}{{\pi }^2}$

The block will separate from plank if the maximum acceleration of SHM is more then 'g'. i.e. ${\omega }^{2}A\ge g$
$\Rightarrow A\ge \frac{g}{{\omega }^2}$ where $\omega =\frac{2\pi }{T}{s}^{-1}=\frac{2\pi }{2}{s}^{-1}=\pi s^{-1}$
$\Rightarrow A\ge \frac{g}{{\pi }^2}$
$\Rightarrow A\ge \frac{10}{{\pi }^2}$ taking $g=10m/s^{-2}$