A bomb of `1kg` is thrown vertically up with speed `100m//s` After 5 seconds it explodes into two parts. One part of mass `400gm` goes down with speed `25m//s` What will happen to the other part just after explosion .

Options

A. `100 ms^(-1)` upward
B. `600 ms^(-1)` upward
C. `100 ms^(-1)` downward
D. `300 ms^(-1)` upward

Answer

A

Explanation

Velocity of particle after 5s
`v = u-gt=100-10xx5`
`=100-50=50ms^(-1)` (upwards)
Conservation of linear momentum gives
`Mv = m_(1)v_(1) + m_(2)v_(2)`................(i)
Taking upward direction positive,
`v_(1) = -25 ms^(-1), v=50ms^(-1)`
`M=1kg, m_(1) = 400g = 0.4Kg`
`m_(2) = M-m_(1) = 1-0.4=0.6kg`
From eq (i),
`1 xx 50=0.4xx(-25)+0.6v_(2)`
or `v_(2) = 100 ms^(-1)` (upwards)`