Question

A free body of mass $8$ kg is travelling at $2$ metre/sec. In a straight line. At a certain instant, the body splits into two equal parts due to internal explosion, which releases $16$ joules of energy. Neither part leaves the original line of motion. Finally?

• A. Both parts continue to move in the same direction as that of the original body
• B. One part comes to rest and the other moves in the same direction as that of the original body
• C. One part comes to rest and the other moves in the direction opposite to that of the original body
• D. One part moves in the same direction and the other in the direction opposite to that of the original body

Answer 1

The correct option is B One part comes to rest and the other moves in the same direction as that of the original body

When the mass splits into two equal parts, the energy released is $16joules$ so, this energy will released as kinetic energy and since both the parts have same mass so, each part will have kinetic energy $8joules$ but both the mass will move in the opposite direction as the linear momentum of the mass has to conserve.

the expression for kinetic energy is $KE=\frac{m{v}^2}{2}$

so, the velocity of each part is,

$v^2=\frac{2\left(KE\right)}{4kg}$

$v=\sqrt{\frac{2\left(KE\right)}{4kg}}$

$v=2m/s$

since, the both parts will move in the opposite direction and the initial velocity of the mass was $2ms$ so, one mass will come to rest and the another will move in the same direction.

So, the correct answer is , B