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Two men each of mass m stand on the rim ...

Two men each of mass m stand on the rim of a horizontal circular disc, diametrically opposite to each other. The disc has a mass M and is free to rotate about a vertical axis passing through its centre of mass. Each mass start simultaneously along the rim clockwise and reaches their original starting positions on the disc. The angle turned through by disc with respect to the ground (in radian) is

Text Solution

Verified by Experts

The correct Answer is:
`2.50`
v= speed relative to rim.
`v- omega R=` speed relative to ground
`L_(i) = L_(f)` as torque about axis of disc is zero.
`rArr 0 + 0 + 0=2m (v- omega R) R- (M)/(2) R^(2) omega`
`rArr 4mv = (4m + M) omega R rArr 300v= 750 omega R`
`rArr 2v= 5 omega R rArr (4pi R)/(t) = (5 theta R)/(t)`
`therefore theta = (4pi)/(5) " radians " therefore N= 2.50`
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