Two block of A and B of mass 1kg and 2kg are hung from light pulley. Initially the block B is held stationary. At `t=0` block B is given velocity 10m//s in upward direction. String and pulley are light and there is no friction anywhere.

Velocity of block 'B' as block 'A' has acended by distance 5m from its original position

Options

A. `10 sqrt(7) m//s`
B. `10/3 sqrt(2) m//s`
C. `10 sqrt(5/3) m//s`
D. `10 sqrt(7)/3 m//s`

Answer

D

Explanation

String will be taught when distance travelled by the two blocks become equal i.e.
`l_(A)=l_(B)Rightarrow1/2g t^(2)=10t-1/2g t^(2)Rightarrowt=1sec.`
Before t=1 sec acceleration of both block will be equation t 'g' in downward direction
After =1 sec, there will jerk in string and velocity of A and B will be given by
`mv_(A)+2mv_(B)=m u_(B)`(u_(A)=velocity of A at t=1 sec)
`Rightarrow v_(A)=u_(A)/3 and v_(A)=u_(A)/3(:.v_(A)=v_(B)`after string becomes thought)
`v_(A)=v_(B)=10//3 m//s`
:. velocity of 'B' when 'A' has ascended by 5m is given by
`v=sqrt((10/3)^(2)+2xx10/3xx10)=10/3sqrt(7)m//s` (:. After t=1sec, a=`10/3 ms^(2))`