question_answer

A bomb of mass 3 m kg explodes into two pieces of mass m kg and 2 m kg. If the velocity of m kg mass is 16 m/s, the total kinetic energy released in the explosion is

A) 192 mJ           

B) 96 mJ

C) 384 mJ           

D) 768 mJ

Correct Answer: A

Solution :

By the conservation of momentum, \[{{m}_{A}}{{\nu }_{A}}\,={{m}_{B}}{{\nu }_{B}}\] \[\Rightarrow \,\,\,\,m \times  16 = 2\,m \times \,\,{{\nu }_{B}}\] \[\Rightarrow \,\,\,\,{{\nu }_{B}} = 8 m/s\]0 Kinetic energy of system \[=\frac{1}{2}\times m\times {{(16)}^{2}}+\frac{1}{2}\times (2m)\times {{8}^{2}}=192\,mJ\]