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?

1 Answer
Mar 14, 2018

#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#