One end of a string is tied to a rigid support attached to roof and the other end is wound around a uniform wheel of radius r and mass m. The string is kept vertical and the wheel is released from rest. As the wheel descends show that (i) the tension in the string is one-third the weight of the wheel, (ii) the magnitude of the acceleration of the centre of mass is 2g/3 and (iii) the speed of the centre of mass is `(4gh//3)^(1//2)`

Explanation

`mg -T = ma, tau = Ialpha, Tr =(1//2) mr^(2)a, a=ralpha, T=(1//2) ma, (3//2) ma = mg, a =2g//3, mgh = (1//2) mv^(2) + (1//2)(1//2)mr^(2)(v^(2)//r^(2)), v=(4gh//3)^(1//2)`