Two discs `A` and `B` are mounted coaxially ona vertical axle. The discs have moments of inertia `l` and `2l` respectively about the common axis. Disc A is imparted an initial angular velocity `2 omega` using the centre potential energy of a spring compressed by a distance `x_(1)`. Disc `B` is imparted angular velocity `omega` by a spring having the same spring constant and compressed by a distance `x_(2)`. Both the disc rotate in the clockwise direction.
The rotation `x_(1)//(x_(2)` is.

Options

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

Answer

C

Explanation

`1/2I(2omega)^(2)=1/2kx_(1)^(2)` and `1/2I(omega)^(2)=1/2kx_(2)^(2)`
dividing then we get
`(x_(1))/(x_(2))=sqrt(2)`