A mass M is supported by a massless string wound around a uniform cylinder of mass M and radius R . On releasing the mass from rest, it will fall with acceleration

Step-by-step solution

The given situation is shown in the figure, We know that, torque, =I If T is the tension in the string, then =T R From Eqs. (i) and (ii), we get I =T R Under no slipping condition, = a R Hence, I a R =T R T= I a R^2 For cylinder, I= M R^2 2 T= M R^2 2 a R^2 T= m a 2 For the motion of the block, aligned & M g-T=M a & M g- M a 2 =M a & M g= 3 M a 2 a= 2 g 3 & aligned