A solid cylinder of mass M and radius R rolls down an inclined plane of height h. The angular velocity of the cylinder when it reaches the bottom of the plane will be

Question

A solid cylinder of mass M and radius R rolls down an inclined plane of height h. The angular velocity of the cylinder when it reaches the bottom of the plane will be, 2 R g h, 2 R g h 2, 2 R g h 3, 1 2 R g h

MARKS App · Accepted Answer

Loss in PE = Gain in KE m g h = 1 2 m v 2 + 1 2 T ω 2 v = R ω m g h = 1 2 m R ω 2 + 1 2 m R 2 2 ω 2 g h = 3 4 R 2 ω 2 ⇒ ω 2 = h g h 3 R 2 ⇒ ω = 2 R g h 3

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