Question

an object at rest explodes into two pieces of 3 kg and 5 kg masses the total kinetic energy of the pieces is 12000 then​

Answer 1

The kinetic energy of the first body is 7500J and kinetic energy of the second body is 4500J.

The object explodes into 2 pieces, so we apply the law of conservation of momentum (momentum of both the piece are same).

We know, Kinetic Energy = p²/2m, where p and m are the momentum and masses respectively.

For the first body,

m₁ = 3kg

So, KE₁ = p²/2m₁ = p²/2(3) = p²/6

For the second body,

m₂ = 5kg

So, KE₂ = p²/2m₂ = p²/2(5) = p²/10

Given total kinetic energy is 12000J

So, KE₁ + KE₂ = 12000

⇒  p²/6 + p²/10 = 12000

Multiplying both sides by 60, we get,

⇒ 10p² + 6p² = 720000

⇒ p² = 720000/16

So, Kinetic energy of the first body is : p²/6 = 7500J

And Kinetic energy of the second body is p²/10 = 4500J