Motion of Connected Mass

A point mass is tied to one end of a string which is wound round the solid body [cylinder, pulley, disc]. When the mass is released, it falls vertically downwards and the solid body rotates unwinding the string

m = mass of point-mass,  M = mass of a rigid body

R = radius of a rigid body, I = moment of inertia of rotating body

(1) Downwards acceleration of point mass 

(2) Tension in string  T = mg [I / (I + mR²)]

(3) Velocity of point mass 

(4) Angular velocity of rigid body ω = (2mgh / (I + mR²))^1/2