Question

A body initially at rest explodes into 2 pieces of mass 2M and 3M respectively having a total kinetic energy E. The kinetic energy of piece of mass 2M after the explosion is?

Answer 1

`3/5 E`

Explanation:

Conservation

`2m v_1 + 3m v_2 = 0`

Energy

`E = 1/2(2m)v_1^2 + 1/2(3m) v_2^2`

Solving for `v_1, v_2`

`v_1^2 = 3/5 E/m, v_2^2 = 4/15E/m`

hence

`E_1=3/5 E`

NOTE

`{(2m v_1 + 3m v_2 = 0),(E = 1/2(2m)v_1^2 + 1/2(3m) v_2^2):}`

or

`{(2 v_1 + 3 v_2 = 0),(E/m = v_1^2 + 3/2 v_2^2):}`

or

`{(4 v_1^2 = 9 v_2^2),(E/m = v_1^2 + 3/2 v_2^2):}`

and solving for `v_1^2, v_2^2` we get

`v_1^2 = 3/5 E/m, v_2^2 = 4/15E/m`