A rolling wheel of 12 kg is on an inclined plane at position P and connected to a mass of 3 kg through a string of fixed length and pulley as shown in figure. Consider P R as friction free surface. The velocity of centre of mass of the wheel when it reaches at the bottom Q of the inclined plane P Q will be 1 2 x g h m s - 1 . The value of x (rounded off to the nearest integer) is _____.

Question

A rolling wheel of 12 kg is on an inclined plane at position P and connected to a mass of 3 kg through a string of fixed length and pulley as shown in figure. Consider P R as friction free surface. The velocity of centre of mass of the wheel when it reaches at the bottom Q of the inclined plane P Q will be 1 2 x g h m s - 1 . The value of x (rounded off to the nearest integer) is _____.,

MARKS App · Accepted Answer

If we take the wheel as a ring then its moment of inertia will be, I = M r 2 . Using mechanical energy conservation, M g h - m g h = 1 2 m v 2 + 1 2 M v 2 + 1 2 I ω 2 ⇒ 12 g h - 3 g h = 1 2 3 v 2 + 1 2 12 v 2 + 1 2 12 r 2 v 2 r 2 ⇒ 9 g h = 15 v 2 + 12 v 2 2 ⇒ v = 2 3 g h = 1 2 8 3 g h Therefore, x = 8 3 ≃ 3

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