Question

Two objects having equal masses are moving with uniform velocities of 2 m/s and 6 m/s respectively. Calculate the ratio of their kinetic energies.

Answer 1

Let the masses of the two bodies be (m₁) = m kg and (m₂) = m kg.
Velocity of the first body, (v₁) = 2 m/s
Velocity of the first body, (v₂) = 6 m/s
The required ratio is-
= $\frac{(Kineticenergy{)}_1}{(Kineticenergy{)}_2}=\frac{\frac{1}{2}\left(m_1\right)(v_1{)}^2}{\frac{1}{2}\left(m_2\right)(v_2{)}^2}$

=$\frac{m(2{)}^2}{m(6{)}^2}=\frac{1}{9}$
The ratio of the kinetic energies is, $\frac{(Kineticenergy{)}_1}{(Kineticenergy{)}_2}=1:9$.