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Two discs A and B are mounted coaxiallay...

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

A

2

B

`(1)/(2)`

C

`sqrt2`

D

`(1)/(sqrt2)`

Text Solution

Verified by Experts

The correct Answer is:
C
(c ) For disc A
`(1)/(2) kx_1^2 = (1)/(2)i(2omega)^2`
`rArr kx_1^2 = 2I omega^2….(i)`
For disc B
`(1)/(2) kx_2^2 = (1)/(2)xx2Iomega^2`
`rArr kx_2^2 = I omega^2 …..(ii)`

On dividing (i) and (ii) we get
`(kx_1^2)/(kx_2^2) = (2I omega^2)/(I omega^2) rArr (x_1)/(x_2) = sqrt2`
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