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 .