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Question

A solid sphere of radius R is resting on a smooth horizontal surface. A constant force F is applied at a height h from the bottom. Choose the correct alternative

A
Sphere will always slide whatever be the value of h
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B
Sphere will roll without slipping when h1.4R
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C
Sphere will roll without slipping if h=1.4R
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D
None of the above
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Solution

The correct option is C Sphere will roll without slipping if h=1.4R
Here by Newton's equation we get F=ma...(i)
We know that, τ=Iα
Also for the sphere to roll without sliding, torque about the point O
τo=Fh=(25mR2+mR2)α
Fh=(75mR2×aR)
As for the condition of pure rolling ,a=Rα

Fh=75mRa, Putting the value of a from equation (i) we get,

Fh=75FR

h=1.4R

Hence option C is the correct answer.

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