Two discs A and B are mounted coaxially on a vertical axle. The discs have moments of inertia I and 2I respectively about the common axis. Disc A is imparted an initial angular velocity `2omega` using the entire potential energy of a spring compressed by a distance `x_1`. Disc B is im parted an angular velocity ω by a spring having the same spring constant and compressed by a distance `x_2`. Both the discs rotate in the clockwise direction.The loss of kinetic energy during the above proces is

Options

A. `(I omega^(2))/(2)`
B. `(I omega^(2))/(3)`
C. `(I omega^(2))/(4)`
D. `(I omega^(2))/(6)`

Answer

B

Explanation

Initial kinetic energy:
`K_(1)=(1)/(2)I(2omega)^(2)+(1)/(2)(2I)omega^(2)=3Iomega^(2)`
Final kinetic energy: `K_(2)=(1)/(2)(I+2I)((4omega)/(3))^(2)=(8)/(3)Iomega^(2)`
Loss in kinetic energy:
`DeltaK_("loss")=K_(1)-K_(2)=(3-(8)/(3))Iomega^(2)=(Iomega^(2))/(3)`