Question

A solid sphere of mass $3kg$ is kept on a horizontal surface. The coefficient of static friction between the surfaces in contact is $2/7$. What maximum force can be applied at the highest point in the horizontal direction so that the sphere does not slip on the surface? (in $N$).

Answer 1

Lets assume friction force and applied force are acting on the same direction that is along the motion . Applied force F , friction force $f=\mu mg$ , $I=\frac{2m{r}^2}{5}$

$F+f=m{a}_{cm}$ ..(1)

torque about center

$(F-f)r=I\alpha$..(2)

for no slipping

$a_{c}m=\alpha r$ ...(3)

on solving 3 equation we get

$F=20N$