Question

A boy pushing a ring of mass $2kg$ and radius $0.5m$ with a stick as shown in figure. The stick applies a force of $2N$ on the ring and rolls it without slipping with an acceleration of $0.3$ $m/s^2$. The coefficient of friction between the ground and the ring is large enough that rolling always occurs and the coefficient of friction between the stick and the ring is $\left(P/10\right)$. The value of $P$ is

Answer 1

Let the friction between surface and sphere be $f_s$

Let the friction between stick and sphere be $f_a$

let the N be the normal reaction between sphere and stick

Now $N-f_s=ma$ also N=2 N,

$f_s=1.4N$

writing torque about center

we get $(f_s-f_a)r=I\alpha$

$a=\alpha r$ and $I=m{r}^2$

on solving $f_a=0.8=\mu N$

$\mu =0.4=4/10$ so P=4