Q: A small mass attached to a string rotates on a frictionless table top as shown. If the tension on the string is increased by pulling the string causing the radius of the circular motion to decrease by a factor of 2 , the kinetic energy of the mass will

(a) Increase by a factor of 4

(b) Decrease by a factor of 2

(c) Remain constant

(d) Increase by a factor of 2

Ans: (a)

Sol: As radius of circular path decreases by factor 2 hence Moment of Inertia decreases by factor 4 .

$K.E = \frac{L^2}{2 I}$ ; Where L = angular momentum = constant

$K.E \propto \frac{1}{ I}$

Hence , Kinetic Energy Increase by a factor of 4 .