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A cylinder rotating at an angular speed ...

A cylinder rotating at an angular speed of 50 rev/s is brought in contact with an identical stationary cylinder. Because of the kinetic friction, torques act on the two cylinders, accelerating the stationary one nd decelerating the moving one. If the common magnitude decelerating the moving one. If the common magnitude of the acceleration and deceleration be one revolution per second sqrare, how long will it take before the two cylinders have equal angular speed?

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The correct Answer is:
B
A cylinder is moving with an angular velocity 50 rev/s is brought in contact wikth another idencital cylinder in rest. The first and second cylinder has common acceleration and deceleration as 1rad/s^2 respectively.
let after 1 sec their angular velocity will be same `omega`.
For the first cylinder.
`omega=50-at`
`rarr t=(omega-50)/1`
and for the 2nd cylinder
`rarr omega=alpha_2t`
`rarr t=omega/I`
So, `omega=((omega-50)/(-1))`
`rarr 2omega=50`
`rarr omega=25rev/s`
`rarr t=25/1 sec=25sec`.
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