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Question

# A force F acts tangentially at the highest point of a disc of mass m kept on a rough horizontal plane. If the disc rolls without slipping, the acceleration of centre of the disc is:

A
2F3m
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B
10F7m
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C
zero
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D
4F3m
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Solution

## The correct option is D 4F3mAs force F moves the sphere towards right , the point of contact has a tendency to slip towards right so that static friction( force f shown ) on the sphere will act towards left.Letr: radius of the spherea: linear accelerationSince there is slipping, α=arFor linear motion, F−f=ma ....(1) where f is the frictional forceFor rotational motion, torque about center, τ=Fr+fr=Iα=(12mr2)ar∴F+f=12ma ......(2)From (1) and (2) adding, we get 2F=32ma∴a=4F3m

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