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

Options

A. 2
B. `(1)/(2)`
C. `sqrt(2)`
D. `(1)/(sqrt(2))`

Answer

C

Explanation

Potential energy of spring becomes rotational kinetic energy of the discs.
`(1)/(2)kx_(1)^(2)-(1)/(2)I(2omega)^(2)`
`implieskx_(1)^(2)=4Iomega^(2)" "......(i)`
Similarly we can write for the other disc
`(1)/(2)kx_(2)^(2)=(1)/(2)(2I)omega^(2)`
`implieskx_(2)^(2)=2Iomega^(2)" ".......(ii)`
Dividing equations (i) and (ii).
`(x_(1))/(x_(2))=sqrt2`
Hence option (c) is correct.