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 $\frac{F}{Km}$. Find the value of $K$.

Answer 1

Answer: 4.00

$f=m{a}_1$ .....(1)
$f\times R=\frac{m{R}^2\alpha }{2}$
$\alpha =\frac{2f}{mR}$
$a-\alpha R=a_1$
$a-\frac{2f}{m}=\frac{f}{m}$
$$\begin{gathered} a=\frac{3f}{m} \\ F-\rho =ma \end{gathered}$$
$F-f=m\times \frac{3f}{m}$
$f=\frac{F}{4}$
$a_1=\frac{f}{m}=\frac{F}{4m}$