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A metal sphere of radius r and specific heat c is rotated about an axis passing through its centre at a speed of n rotations per second. It is suddenly stopped and 50% of its energy is used in increasing its temperature. Then the rise in temperature of the sphere is

Options

  1. A2 5 π 2 n 2 r 2 c
  2. B1 10 π 2 n 2 r 2 c
  3. C7 8 π r 2 n 2 c
  4. D1 8 π 2 n 2 r 2 c

Correct answer

A. 2 5 π 2 n 2 r 2 c

Step-by-step solution

Specific heat of metal = C Temperature change = θ Here, 50 100 ( K E of rotation) = c m θ 1 2 ( 1 2 I ω 2 ) = C m θ, ⇒ 1 4 ( 2 5 m r 2 ) ( 2 π n ) 2 = C m θ ⇒ θ = 2 5 π 2 n 2 r 2 c

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