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. `sqrt2`
D. `(1)/(sqrt2`

Answer

C

Explanation

When a spring is compressed,by a distance x, the P.E. stored in it used to rotate the disc with some angular velocity `(omega)` and gets the rotational K.E.`=(1)/(2)Iomega^(2)`
Thus for the disc `A,(1)/(2)K x_(1)^(2)=(1)/(2)I(2omega)^(2)" ...(1)"`
For the disc B, `(1)/(2)K x_(2)^(2)=(1)/(2)(2I)omega^(2)" ...(2)"`
`therefore" "(x_(1)^(2))/(x_(2)^(2))=(2Iomega^(2))/(Iomega^(2))=2`
`therefore" "(x_(1))/(x_(2))=sqrt2`