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In the following figure all surfaces are...

In the following figure all surfaces are assumed to be frictionless and pulley us assumed to be ideal. The block 'A' is projected towards the pulley 'P' with an intial velocity `u_(0)` then select correct option :

A

the string would become tight at `t =(2u_(0))/(g)`

B

the distance travelled by 'A' before the string is taut is `(u_(0)^(2))/(g)`

C

the distance travelled by 'B' before string is taut is `(2u_(0)^(2))/(g)`

D

the common speed of the blocks just after the string is taut is `((n+2)/(n+1))u_(0)`

Text Solution

Verified by Experts

The correct Answer is:
A, C, D
When the strin is taut again both the block would travel the same distance
hence `u_(0)t = (1)/(2)g t^(2) [" as 'B' is falling freely"]`
Hence `t = (2u_(0))/(g)` in this time 'A' and 'B' would travel a distance of `(2u_(0))/(g)`
also when same impulse acts along the wire the change in momentum would be same for both blocks.
`J = nmv - nmu_(0)` (for block A)
`-J = mv - m(2u_(0))` (for block B)
`nmv - nmu_(0) = 2mu_(0) - mv`
`(n + 1) v = (n + 2) u_(0)`
`v = ((n + 2)/(n + 1)) u_(0) rArr J = nmv - nmu_(0)`
`-J = mv - m(2u_(0)) rArr nmv - nmu_(0)`
`= 2mu_(0) - mvrArr (n + 1) v = (n + 2)u_(0)`
`v = ((n + 2)/(n + 1)) u_(0)`
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