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Two unequal masses of 1 kg and 2 kg are ...

Two unequal masses of 1 kg and 2 kg are attached at the two ends of a light inextensible string passing over a smooth pulley as shown . If the system is released from rest, find the work done by string on both the blocks in 1 s.
(Take `g= 10 m//s^2`).

A

The angular acceleration of shaft C is in clockwise direction as seen from the side of A and remains constant

B

The angular acceleration of shaft C is in clockwise direction as seen from the side of A and is decreasing with time

C

The angular velocity of the shaft when the block of mass 20 kg has fallen by 5m is 28.28 rad/s

D

The linear tangential velocity with which the cord is wrapped up from B at the instant described in option (C) is 7.07 m/s

Text Solution

Verified by Experts

The correct Answer is:
A, C, D
`(T_(1) - T_(2)) R = 2, 1/2 5R^(2)alpha`
`20 - T_(1) = 2 a`
`T_(2)-5g = 5a`, `a = R alpha`

`rArr 15g = 30 a rArr a=5m//s^(2)`
and `alpha = 5/(0.25) = 20 md//s^(2)` clockwise as seen from side of A
`(S = ut + 1/2at^(2)),5 = 1/2(5)t^(2) rArr t=sqrt(2)` sec
`(omega_(t) = omega_(i) + alpha t), omega_(f) = 20 xx sqrt(2) = 28.28 rad//s`.
`(V= u + at), V = 5sqrt(2) = 7.07 m//s`
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