Question

A Stationary body explodes into two fragments of masses m1 and m2. If the momentum of one fragment is P then energy of explosion is ..?

Answer 1

first , we should apply law of conservation of linear momentum,
e.g., initial linear momentum = final linear momentum
or, (m1 + m2) × 0 = P1 + P2

or, P1 = -P2

a/c to question, momentum of one fragment is P
if P1 = P then, P2 = -P

now, kinetic energy of first fragment, E1 = P²/2m1 [ as kinetic energy = (linear momentum)²/2 × mass ]
kinetic energy of 2nd fragment, E2 = (-P)²/2m2 = P²/2m2

so, total kinetic energy of fragments = E1 + E2
= P²/2m1 + P²/2m2

hence, energy of explosion = P²/2m1 + P²/2m2