Question

A disc of mass $m$ and radius $R$ is placed over a plank of same mass $m$. There is sufficient friction between the disc and the plank to prevent slipping. A force $F$ is applied at the centre of the disc. Then, the acceleration of the plank is $\frac{F}{K m}$. Find the value of $K$.

Answer 1

$f =m a_{1} $ .....(1)
$f \times R =\frac{m R^{2} \alpha}{2} $
$\alpha=\frac{2 f}{m R}$
$ a-\alpha R =a_{1} $
$ a-\frac{2 f}{m} =\frac{f}{m} $
$a =\frac{3 f}{m} \\ F-\rho=m a $
$F-f =m \times \frac{3 f}{m} $
$ f =\frac{F}{4} $
$ a_{1}= \frac{f}{m}=\frac{F}{4 m} $