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Question

# A disc of mass m and radius R rolls down an inclined plane of height h without slipping. Find out the velocity of the disc when it reaches the bottom of the incline? The moment of inertia for a disk is (1/2)mR2.

A
gh
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B
43gh
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C
2gh
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D
2gh
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E
22gh
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Solution

## The correct option is A √43ghInitial kinetic energy of the system is zero as the system is at rest initially.Moment of inertia for a disk about its center I=12mR2As there is no slipping, thus v=Rw .................(1)Using work-energy theorem : W=ΔK.E∴ mgh=12mv2+12Iw2−0OR mgh=12mv2+12×mR22×v2R2 (using (1))OR mgh=34mv2 ⟹v=√43gh

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