On the surface of a solid cylinder of mass 2 kg and radius 25 cm a string is wound several times and the end of the string is held stationary while the cylinder is released from rest. What is the acceleration of the cylinder and the tension in the string ?

Explanation

Let a be the acceleration of the centre of mass. Then mg -T = ma……(i)
where Tis the tension in the string. (See Fig.) For the rotational motion about the centre of mass,
`tau = l alpha`
`Tr = 1/2 mr^(2) alpha`………(ii)
But `a = r alpha`
`T =1/2 mr a/r =1/2 ma`.......(iii)
From eqns (i) mg-T = ma
`mg -1/2 ma = ma`
`3/2 ma = mg`
`a =(2g)/3 = (2 xx 9.8)/3 = 6.53 m//s^(2)`
`T = 1/2 ma = 1/2 xx 2 xx (19.6)/3 = 6.53 N`