A bomb of mass `3.0 kg` explodes in air into two pieces of masses `2.0 kg` and `1.0 kg`. The smaller mass goes at a speed of `80 m//s`. The total energy imparted to the two fragments is :

Options

A. `1.07 kJ`
B. `2.14 kJ`
C. `2.4 kJ`
D. `4.8 kJ`

Explanation

Both fragments will posses the equal linear momentum
`m_(1) v_(1) = m_(2) v_(2) implies 1 xx 80 = 2 xx v_(2) implies v_(2) = 40 m//s`
`:.` Total energy of system
` = (1)/(2) m_(1) v_(1) + (1)/(2) m_(2) v_(2)^(2)`
`= (1)/(2) xx 1 xx (80)^(2) + (1)/(2) xx 2 xx (40)^(2)`
`= 4800 J = 4.8 kJ`