A body of mass 1 kg is projected vertically upwards wit a speed of 100 m/s. After 6 s it explodes into two parts. One part of mass 400 g comes back with speed 25 m/s. What is the velocity of other part just after explosion?

Options

A. 83.3 m/s upward
B. 600 m/s upward
C. 100 m/s downward
D. 300 m/s upward

Answer

A

Explanation

Momentum of the shell before explosion `= MV = ( m_(1) + m_(2)) V`
Momentum after collision `= m_(1) V_(1) + m_(2) V_(2)`
By the principle of conservation of linear momentum
`(m_(1)+m_(2))V = m_(1)V_(1)+m_(2)V_(2)`
`:. ( m_(1)+m_(2))xx 500 = m_(1) xx 600 xx m_(2) xx 200`
`500m_(1) + 500 m_(2) = 600 m_(1) + 200 m_(2)`
`:. ( 500- 200) m_(2) = ( 600 - 500) m_(1)`
`:. 300 m_(2) = 100m_(1)`
`:. ( m_(1))/( m_(2)) = ( 300)/( 100) = 3:1 `