Question

A light body and a heavy body have same kinetic energy. Which one has greater linear momentum

Answer 1

The momentum of the heavier body is greater .

Let the mass of the light body = m1 and it's velocity = v1

Let the mass of heavy body = m2 and it's velocity = v2

Both bodies have the same kinetic energy -

Therefore ,

=> 1/2 m1 × (v1)² = 1/2 m2×(v2)²

=> m1 (v1)² = m2 (v2)²

Momentum = mv = p

P1 = momentum of m1

P2 = momentum of m2

=> m1²( v1)² /m1 = m2² (v2)² /m2

=> (p1)²/m1 = (p2)²/m2

=> p1/p2 = √(m1/m2)

p1 < p2

p1 is less than p2 as the value of m1 is less than m2.

Momentum of the heavier body is greater.