A mental 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 raise in temperature of the sphere is

Step-by-step solution

Rotational KE of sphere = 1 2 I ^2 For sphere, I= 2 5 m r^2 aligned & KE & = 1 2 2 5 m r^2(2 n)^2= 1 5 m r^2 4 ^2 n^2 & = 4 5 m r^2 ^2 n^2 ~J & Heat produced Q= 1 2 KE & = 1 2 ( 4 5 m r^2 ^2 n^2 ) & = 2 5 m r^2 ^2 n^2 & Q=m s t & In temperature & aligned aligned t & = Q m s = 2 5 m r^2 ^2 n^2 m s & = 2 5 r^2 ^2 n^2 s aligned