Question

Two bodies of mass one kg and 4 kg have equal momemtum. What is ratio of their kinetic energy

Answer 1

Mass (m1) = 1kg

Velocity = v

Momentum = mv = v

Kinetic energy(k1) = ½v²

Mass (m2) = 4kg

Velocity = V

Momentum = mv = 4V

Kinetic energy(k2) = ½mV²

= ½×4×V²

=> 2V²

A/Q,

v= 4V

v/V= 4:1

v²/V² = 16:1 .....(i)

Kinetic energy (k1)/kinetic energy (k2)

=>½v²/2V²

=>½×16/2×1 {from eq(i)}

=> 8/2

=>4:1

Ratio of their kinetic energy = 4:1

Cheers!