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Question

A force 10 N acts tangentially at the highest point of a solid sphere of mass 10 kg kept on a rough horizontal plane. If the sphere rolls without slipping, find the acceleration of the centre of the sphere (in m/s2).


A
53
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B
35
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C
710
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D
107
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Solution

The correct option is D 107

The sphere will have a tendency to slip towards left at the point of contact, thus friction will act rightwards as shown.
Since the sphere is rolling without slipping, a=αR . . . (1)

From Fext=macom
F+f=ma ...(2)
and from τextcom=Icomα
F×R+f×R=25mR2×α
Ff=25mRα ...(3)

From (1), (2) & (3)
2F=ma+25ma=75ma
a=10F7m=10×107×10=107 m/s2

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