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Question

A solid sphere of mass m is lying at rest on a rough horizontal surface. The coefficient of friction between the ground and sphere is μ. The maximum value of F, so that the sphere will not slip, is equal to

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A
75μmg
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B
47μmg
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C
57μmg
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D
72μmg
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Solution

The correct option is D 72μmg
For translational motion: ma=Ff where f=μmg
Thus ma=Fμmg .......(1)
For rotational motion: net torque about O, τ=Iα
fR=25mR2(α) .........(2)
Also as the sphere does not slip, thus a=rα
Equation (2) becomes , μmgR=25mR2aR
ma=52μmg
Put it in (1), 52μmg=Fμmg
F=72μmg

438120_159544_ans.png

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