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Initial angular velocity of a circular d...

Initial angular velocity of a circular disc of mass `M` is `omega_(1)`. Then two small spheres of mass `m` are attached gently to two diametrically opposite points on the edge of the disc. What is the final angular velocity of the disc -

A

`((M +m)/(M)) omega_(1)`

B

`((M +m)/(m)) omega_(1)`

C

`((M )/(M + 4m)) omega_(1)`

D

`((M )/(M + 2m)) omega_(1)`

Text Solution

Verified by Experts

The correct Answer is:
C
Conservation of angular momentum gives
`(1)/(2) MR^(2) omega_(1) = ((1)/(2) MR^(2) + 2 MR^(2)) omega_(2)`
`rArr (1)/(2) MR^(2) omega_(1) = (1)/(2) R^(2) (M + 4m) omega_(2)`
:. `omega` `= ((M)/(M + 4m)) omega_(1)`.
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