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The pulley in the diagram are all smooth...

The pulley in the diagram are all smooth and light. The acceleration of `A` is a upwards and the acce,leration of `C` is `f` downwards. The acceleration of `B` is

A

`½(f-a) up`

B

`½(a+f)down`

C

`½(a+f)up`

D

`½(a-f)up`

Text Solution

Verified by Experts

The correct Answer is:
A
`l_(1) +2l_(2) +l_(3) =` constant ltbrltgt `(dl_(1))/(dt) +2(dl_(2))/(dt) +(dl_(3))/(dt) = 0`
`(d^(2)l_(1))/(dt^(2)) +2(d^(2)l_(2))/(dt^(2)) +(d^(2)l_(3))/(dt^(2)) = 0`
`rArr -a +2a_(B) +f = 0`
`a_(B) =- (1)/(2) (f-a) rArr a_(B) = (1)/(2) (f-a) uarr`
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