A shell of mass 2 kg and moving at a rate of 4 m/s suddenly explodes into two equal fragments. The fragments go in directions inclined with the original line of motion with equal velocities. If the explosion imparts 48 J of translational kinetic energy to the fragments divided equally, the velocity (magnitude and direction both) of each fragment :-

Options

A. 2 m/s , `45^@`
B. 8 m/s , `45^@`
C. 8 m/s , `60^@`
D. 2 m/s , `60^@`

Answer

C

Explanation

Initial horizontal momentum = Final horizontal momentum
2 kg x 4m/s = 1kg x v cos `theta` m/s+1 kg x v cos `theta` m/s

`8 = 2v cos theta`
`v cos theta` = 4 m/s ….(i)
The initial kinetic energy of the shell
`=1/2xx2kgxx(4m//s)^2`
=16 J
An amount of 48 J is imparted by explosion. Thus, the total energy of the fragments is 64 J, i.e. each fragment has 32 J kinetic energy
`=1/2xx 1kg xx v^2 `=32 J
`v^2`=64
v=8m/s
and `v cos theta `=4
`cos theta =1/2 rArr theta =60^@`