Two discs `A` and `B` each of mass `2kg` and radius `0.5m` are rigidly fixed to the end of a thin shaft `S`, which is supported in horizontal position with the help of two smooth bearings at points `P_(1)` and `P_(2)`. Two blocks of masses `2 kg` and `1 kg` are connected to the light cords wrapped around the discs as shown in the figure. There is no slipping between the cord and the discs. If the system is released from rest from the position shown, the mark released from rest from the position shown,

Options

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

Answer

A, C, D

Explanation

`(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`