A thin circular metal disc of the radius 500 mm is set rotating about a central axis normal to its plane. Upon raising in temperature gradually, the radius increases to 507 . 5 mm . The percentage change in the rotational kinetic energy will be

Step-by-step solution

Given dR R × 100 = 507.5 - 500.0 500.0 × 100 = 1.5% Now, K = 1 2 I ω 2 = 1 2 I I ω 2 = L 2 2 I or, K = L 2 2 MR 2 2 = L 2 M R 2 Taking log and differentiating, dK K = - 2 dR R or, the percentage change in K = dK × 1 0 0 K = - 2 dR R × 1 0 0 = - 3 %