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Question

# A horizontal force F acts on a solid sphere of mass M at its centre. Coefficient of friction between the ground and sphere is μ. Let the maximum force F for which there is no slipping be n2μMg. Find n.

A
5
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B
7
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C
6
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D
3
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Solution

## The correct option is B 7For linear motion of sphere, F−f=Ma.......(1) For pure rolling motion: a=Rα⇒α=aR For rotational motion about the center of the sphere: τ=Iα ⇒fR=Iα ⇒fR=25MR2×aR (∵I=25MR2 for sphere) ⇒f=25Ma ⇒Ma=52f......(2) Putting equation (2) in equation (1) F−f=52f ⇒f=27F For no slipping, f≤μMg 2F7≤μMg F≤72μMg Thus, n=7.

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