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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

b

47μmg

c

57μmg

d

72μmg

answer is D.

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Detailed Solution

As sphere is rolling we can apply torque equation about point of contact (about P).FR=IPα⇒ FR=75MR2α⇒ Rα=5F7M=aEquation of translatory motionF−f=Ma⇒f=27F   ………(i)For no sliding, f≤μmg ⇒ F=72μmg
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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