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A child with mass m is standing at the e...

A child with mass `m` is standing at the edge of a disc with moment of inertia `I`, radius `R`m and initial angular velocity `omega`. See figure given below. The chlid jumps off the edge of the disc with tangential velocity `v` with respect to the ground. The new angular velocity of the disc is.
.

A

`sqrt((I omega^(2) - mv^(2))/(I))`

B

`sqrt(((I + mR^(2)) omega^(2) - mv^(2))/(I))`

C

`(I omega-mvR)/(I)`

D

`((I +mR^(2)) omega - mvR)/(I)`

Text Solution

Verified by Experts

The correct Answer is:
D
From conservation of linear momentum
`(I + mR^(2)) omega = mvR + I omega'`
`omega' ((I +mR^(2)) omega -mvR)/(I)`.
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Knowledge Check

  • A child with mass m is standing at the edge of a merry go round having moment of inertia I , radius R and initial angular velocity omega as shown in the figure. The child jumps off the edge of the merry go round with tangential velocity v with respect to the ground. The new angular velocity of the merry go round is

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