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Q.

A solid sphere, solid cylinder and a disc are allowed to roll down from the top of an incline plane from the same height. Then

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a

Disc will reach the bottom first

b

Solid cylinder will reach the bottom first

c

Sphere will reach the bottom first

d

All will reach the bottom simultaneously

answer is C.

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Detailed Solution

Acceleration of a round object rolling without slipping down a rough inclined surface having inclination θ with horizontal is given by a = gsinθ / (1+ Ic /mr2)For solid sphere, Ic = 2/5 mR2.: a1 = 5/7 g sin θFor solid cylinder , Ic  = 1/2 mR2.: a2 = 2/3 g sin θFor Solid disc , Ic = 1/2 mR2.: a3 = 2/3 gsinθSince a1 > a2 = a3 , option - (3) is correct.
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