A solid sphere is in rolling motion. In rolling motion a body possesses translational kinetic energy K t as well as rotational kinetic energy K r simultaneously. The ratio K t : K t + K r for the sphere is

Question

A solid sphere is in rolling motion. In rolling motion a body possesses translational kinetic energy K t as well as rotational kinetic energy K r simultaneously. The ratio K t : K t + K r for the sphere is, 10 : 7, 5 : 7, 7 : 10, 2 : 5

MARKS App · Accepted Answer

Transnational K E = 1 2 m v 2 Translational K E + Rotational K E = 1 2 m v 2 + 1 2 I ω 2 = 1 2 m v 2 + 1 2 ( 2 5 m r 2 ) ω 2 ∵ for rolling motion v = r ω = 1 2 m v 2 + 1 2 × 2 5 m r 2 ( v r ) 2 = 7 10 m v 2 So, K t K t + K r = 1 2 m v 2 7 10 m v 2 = 5 7

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