Q96 / 180 · NEET 2018 · Physics

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

  • A
    10 : 7
  • Correct answer
    B
    5 : 7
  • C
    7 : 10
  • D
    2 : 5

Solution

Transnational KE = 1 2 m v 2
Translational KE+ Rotational KE
= 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=rω
= 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

Hence, the correct answer is option: 'B'.

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