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A metal sphere of radius r and specific heat S 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 π 2 n 2 r 2 5 S
  2. Bπ 2 n 2 10 r 2 S
  3. C7 8   π r 2 n 2 S
  4. D5 π r n 2 14 S

Correct answer

A. 2 π 2 n 2 r 2 5 S

Step-by-step solution

I = 2 5 m r 2 , ω = 2 π n k = 1 2 I ω 2 = 1 2 × 2 5 m r 2 × 4 π 2 n 2 = 4 5 π 2 m r 2 n 2 Δ θ = Δ Q m S = k 2 m S = 2 5 π 2 m r 2 n 2 m S = 2 π 2 r 2 n 2 5 S

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