A bomb of mass 16kg at rest explodes into two pieces of masses 4 kg and 12 kg. The velolcity of the 12 kg mass is `4 ms^-1`. The kinetic energy of the other mass is

Options

A. `144 J`
B. `288 J`
C. `192 J`
D. `96 J`

Answer

B

Explanation

On applying law of conservation of linear momentum
`vec(P)_(1) = vec(P)_(f) rArr 16 xx vec(0) = 4vec(v)_(4) + 12 xx 4 hat(i) rArr vec(v)_(4) = 12 (-hat(i))`
The `4 lg` block will move in a direction opposite to `12 kg` block with a speed of `12 m//s`. The corresponding kinetic energy of `4 kg` block
`= (1)/(2) xx 4 xx (12)^(2) = 288 J`