Question

A bike of mass $100kg$ and a car of mass $500kg$ are moving at the same speed. Find the ratio of their kinetic energies.

Answer 1

Step 1: Given data,

Mass of the bike, $m_b=100kg$

Mass of the car, $m_c=500kg$

Their velocities, $v_c=v_b=v$

Step 2: Finding ratio of kinetic energies,

The formula for the kinetic energy of a body is $K=\frac{1}{2}m{v}^2$.

Putting values,

kinetic energy of car, $K_c=\frac{1}{2}\times 100\times v^2$

kinetic energy of , $K_b=\frac{1}{2}\times 500\times v^2$

Ratio of kinetic energies, $\frac{K_b}{K_c}=\frac{{\displaystyle \frac{1}{2}}\times 100\times v^2}{\frac{1}{2}\times 500\times v^2}=\frac{1}{5}$

Hence, the ratio of their kinetic energies is $\frac{1}{5}$.