In the figure shown, acceleration with which the mass m falls down when released is (consider the string to be massless, g -acceleration due to gravity)

Step-by-step solution

Let tension in string is T and tension T is rotating the hollow cylinder. Torque produced in hollow cylinder, =I Moment of inerita of cylinder, I=M R^2 where, M= mass of cylinder and R= radius of cylinder. Angular acceleration, = a R , where a= acceleration. Equating Eqs. (i) and (ii), we get T R=M R a T=M a Now, M g-T=M a aligned & M g-M a=M a 2 M a=M g a= & g / 2 aligned