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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 7
For linear motion of sphere,
Ff=Ma.......(1)
For pure rolling motion:
a=Rαα=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)
Ff=52f
f=27F
For no slipping, fμMg
2F7μMg
F72μMg
Thus, n=7.

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