Question

A sphere of mass $m$ is given some angular velocity about a horizontal axis through its centre and gently placed on a plank of mass $m$ as shown in figure. The coefficient of friction between sphere and plank is $\mu$. If the plank rests on a smooth horizontal surface,the initial acceleration of the sphere relative to the plank is equal to _____

• A. zero
• B. $\mu g$
• C. $\left(\frac{7}{5}\right)\mu g$
• D. $2\mu g$

Answer 1

The correct option is D. $2\mu g$.

From Free Body diagram of sphere
$m{a}_{sphere}=\mu mg$
$a_{sphere}=\mu g$
From Free Body diagram of plank
$m{a}_{plank}=-\mu mg$
$a_{plank}=-\mu g$
Acceleration of sphere wrt plank is
$a_{rel}=a_{sphere}-a_{plank}$
$a_{rel}=2\mu g$