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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).

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Solution

Lets assume friction force and applied force are acting on the same direction that is along the motion . Applied force F , friction force f=μmg , I=2mr25
F+f=macm ..(1)
torque about center
(Ff)r=Iα..(2)
for no slipping
acm=αr ...(3)
on solving 3 equation we get
F=20N

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