Question

Two bodies of equal masses are moving with uniform velocities v and 2v. Find the ratio of their kinetic energies.

April 18, 2024

Answer

Velocity of first body v₁ = v

Velocity of second body, v₂ = 2v

As the mass of the two bodies are same and as kinetic energy is directly proportional to the square of the velocity (K α v²)

Hence, ratio of their kinetic energies is

$K_1\over K_2$ = $(v_1)^2\over (v_2)^2$

⇒ $K_1\over K_2$ = $(v)^2\over (2v)^2$

⇒ $K_1\over K_2$ = $v^2\over 4v^2$

⇒ $K_1\over K_2$ = $1\over 4$

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