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Question

A solid uniform disk of mass m rolls without slipping down a fixed inclined plane with an acceleration a. The frictional force on the disk due to surface of the plane is?

A
2 ma
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B
3/2 ma
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C
ma/2
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D
1/2 ma
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Solution

The correct option is C ma/2
Here as the sphere is rolling down an inclined plane it will produce a torque τ=Iα where I = moment of inertia and α=angular acceleration
Now the frictional force f=Nμs
Where N=normal force=mgcosθ and μs=static friction
We also know moment of inertia of sphere I=12mR2;where R=radius of sphere.
and α=acceleration(a)R
In the given case torqueτ=frictional forcef×R
fR=Iτ
fR=12mR2aR
f=ma2

1149118_1105034_ans_8b84e2b41c6e47598e30671802d25cf4.jpg

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