The system in Fig. is released from rest from the position shown. After blocks have moved distance `H//3`. collar `B` is removed and block `A` and `C` continue to move. The speed of `C` just before it strikes the ground is

Options

A. `4/3sqrt(gH)`
B. `2(sqrt(gH))/3`
C. `sqrt((13gH))/3`
D. `2sqrt(2gH)`

Answer

C

Explanation

Initial acceleration of the system before the collar is removed.
`a_(1)=(2mg)/(3m)=(2g)/3`
velocity at the time when the collar is removed:
`v_(1)=sqrt(2a_(1)H/3)`
Acceleration after the collar is removed
`a_(2)=(mg)/(2m)=g/2`
Final velocity `=v_(2)^(2)=v_(1)^(2)+2a_(2)H`
`=(2a_(1)H)/3+(2g)/2H=2/3 (2g)/3H+gH`
`implies v_(2)=sqrt((13gH)/3`