A uniform solid sphere of radius R and radius of gyration K about an axis passing through the centre of mass, is rolling without slipping. Then the fraction of total energy associated with its rotation will be

Question

A uniform solid sphere of radius R and radius of gyration K about an axis passing through the centre of mass, is rolling without slipping. Then the fraction of total energy associated with its rotation will be, K 2 + R 2 K 2, K 2 R 2, K 2 K 2 + R 2, R 2 K 2 + R 2

MARKS App · Accepted Answer

in pure rolling motion Rotational KE K R = 1 2 m K 2 ω 2 = 1 2 m v 2 K 2 R 2 Total KE K E = 1 2 m v 2 1 + K 2 R so K R K E = 1 2 m v 2 K 2 R 2 1 2 m v 2 1 + K 2 R 2 = K 2 K 2 + R 2

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