Question

A bomb of mass 10Kg explodes into two pieces of masses 4Kg and 6Kg . If kinetic energy of 4Kg piece is 200J. Find out kinetic energy of 6Kg piece

A.)400/3J B.)200/3J. C.)100/3J. D.)300/5J

Answer 1

mass of the bomb M = 10kg initial velocity of the bomb = 0 m/s mass of the smaller piece = 4 kg= m1 (say) Kinetic energy of smaller piece just after explosion=200J therefore 1/2 mv^2 = 200J [1 Joule is equivalent to 1kg*(m/s)^2] 1/2*4v^2 = 200 2v^2 = 200 v = 10 m/s Hence, Velocity of 4kg piece after explosion v= 10m/sec mass of the bigger piece =6kg=m2 (say) let, velocity of the bigger piece just after explosion= v1 as there is no external force is acting on the bomb intially so the momentum is conserved in all direction. i.e P(just after explosion)=P(just before explosion) m1*v + m2*v1 = M*0 4*10 + 6*v1 =0 =>v1 = -40/6 = -20/3m/s so the kinetic energy of the 6kg piece = (1/2)*m2*v1*v1 Joule =(1/2)*6*400/9 =400/3 Joule Ans.