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 imparted an angular velocity `omega` by a spring having the same spring constant and compressed by a distance `x_(2)`. Both teh 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

Here K.E. of rotation = P.E. of the spring
`therefore (1)/(2)I(2omega)^(2)=(1)/(2)kx_(1)^(2)`
and `(1)/(2)xx2Iomega^(2)=(1)/(2)kx_(2)^(2)`
Dividing `(x_(1)^(2))/(x_(2)^(2))=2and(x_(1))/(x_(2))=sqrt(2)`