A shell of mass 2 kg and moving at a rate of 4m/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 equall, the velocity (magnitude and direction both) of each fragment:

Options

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

Answer

C

Explanation

Initial horizontal momentum `=` Final horizontal momentum
`2kgxxr4//m//s=1kgxxv cos thetam//+1kgxxvcos 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)`
`=16J`
An amount of 48J is imparted by explosion. Thus, the total energy of the fragments is 64J, i.e. each fragment has 32 J kinetic energy.
`=1/2xx1kgxxv^(2)=32J`
`v^(2)=64`
`v=8m//s`
and `v cos theta=4`
`cos theta =1/2impliestheta=60^(@)`