The angular speed of cylinder is proportional to h^n, where h is the height through which mass falls, Then the value of n is___

Question

A solid cylinder of mass M and R is mounted on a frictionless horizontal axle so that it can freely rotate about this axis. A string of negligible mass is wrapped round the cylinder and a body of mass m is hung from the string as shown in figure the mass is released from rest then___

The angular speed of cylinder is proportional to hⁿ, where h is the height through which mass falls, Then the value of n is___ 

(A) zero 

(B) 1 

(C) (1/2) 

(D) 2

Answer 1

Correct option: (C) (1/2)

Explanation:

Angular velocity = ω = √[(2mgh) / (I + mR²)]

ω ∝ √h = h^(1/2) 

hence n = (1/2)