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As shown in the figure, two bobs of mass...

As shown in the figure, two bobs of masses m & 2m are tied by a massless string which is wound on a fly wheel (disc) of radius r and mass m. When released from rest the bob of mass 2m starts falling vertically. When it has covered distance of h, the angular speed of the wheel will be:

A

`r sqrt((3)/(2gh))`

B

`(1)/(r ) sqrt((7gh)/(3))`

C

`(1)/(r ) sqrt((4gh)/(7))`

D

`r sqrt((3)/(7gh))`

Text Solution

Verified by Experts

The correct Answer is:
C
Loss in P.E. = Gain in K.E.
`2mg h- mgh = (1)/(2) mv^(2) = (1)/(2) mv^(2) + (1)/(2) I omega^(2) rArr mgh = (3)/(2) m omega^(2) r^(2) + (1)/(2).(mr^(2))/(2).omega^(2)`
`rArr mgh = (7)/(4) m omega^(2) r^(2), omega = sqrt((4gh)/(7r^(2)))= (1)/(r ) sqrt((4gh)/(7))`
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