A solid sphere is in rolling motion. In rolling motion a body possesses translational kinetic energy $ \left(K_{t}\right) $ as well as rotational kinetic energy $ \left(K_{r}\right) $ simultaneously. The ratio $ K_{t}:\left(K_{t}+K_{r}\right) $ for the sphere is

Question

A solid sphere is in rolling motion. In rolling motion a body possesses translational kinetic energy $ \left(K_{t}\right) $ as well as rotational kinetic energy $ \left(K_{r}\right) $ simultaneously. The ratio $ K_{t}:\left(K_{t}+K_{r}\right) $ 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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