A body of mass `50 kg` is projected vertically upward with velocity of `100 m//s`. After `5 s` this body breaks into `20 kg` and `30 kg`. If the `20 kg` piece travels upwards with `150 m//s`, then the velocity of other block will be

Options

A. 15 m/sec downwards
B. 15 m/sec upwards
C. 51 m/sec downwards
D. 51 m/sec upwards

Answer

A

Explanation

Velocity of 50 kg mass after 5 sec of projection `v=u -g t= 100- 9.8 xx 5= 51 m//s`
At this instant momentum of body is in upward direction `P_("initial")= 50 xx 51= 2550 kg- m//s`
After breaking 20kg piece travels upwards with 150 m/s let the speed of 30 kg mass is V
`P_("final")= 20 xx 150 + 30 xx V`
By the law of conservation of momentum
`P_("initial")= P_("final")`
`rArr 2550 = 20 xx 150 + 30 xx V rArr V= -15 m//s`
i.e. it moves in downward direction.