First slide

Rolling motion

Question

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

Moderate

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

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+ I_c /mr²)
For solid sphere, I_c = 2/5 mR²
.: a₁ = 5/7 g sin θ
For solid cylinder , I_c= 1/2 mR²
.: a₂ = 2/3 g sin θ
For Solid disc , I_c = 1/2 mR²
.: a₃ = 2/3 gsinθ
Since a₁ > a₂ = a₃ , option - (3) is correct.

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