Question

Two bodies have masses in the ratio 5 : 1 and
kinetic energies in the ratio 125 : 9. Calculate the
ratio of their velocities.
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Answer 1

Answer:

Ratio of the mass of the body = 5 : 1`

Ratio of the Kinetic Energy of the body = 125/9

Since, K.E. = 1/2 mv²

Therefore, Ratio of K.E.₁ : K.E.₂ = m₁v₁²/m₂v₂²

∴ v₁²/v₂² = K.E.₁/K.E.₂ × m₂/m₁

∴ v₁²/v₂² = 125/9 × 1/5

∴ v₁²/v₂² = 25/9

∴ v₁/v₂ = 5/3

Hence, the ratio of the velocity of the body a to the velocity of the body b is 5 : 3.

Hope it helps.