A shell of mass `20 kg` at rest explodes into two fragments whose masses are in the ratio `2 : 3`. The smaller fragment moves with a velocity of `6 m//s`. The kinetic energy of the larger fragment is

Options

A. 96 J
B. 216 J
C. 144 J
D. 360 J

Answer

A

Explanation

Total mass of the shell = 20 kg
Ratio of the masses of the fragments `= 2:3`
`therefore `Masses of the fragments are 8 kg and 12 kg
Now, according to the conservation of momentum
`m_1 v_1 = m_2 v_2`
`therefore 8 xx 6 = 12 xx v`
v (velocity of the larger fragment) = 4m/s
Kinetic energy `=1/2 mv^2`
`= 1/2 xx 12 xx (4)^2 = 96 J`