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 :

Options

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)`

Answer

A, C, D

Explanation

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)`