Question

Two bodies of equal mass move with uniform velocities $v$ and $4v$. Find the ratio of their kinetic energies.

• A. $1:4$
• B. $4:1$
• C. $1:16$
• D. $16:1$

Answer 1

The correct option is C $1:16$

Kinetic energy of the body $K=\frac{1}{2}m{v}^2$

For same mass $m$, $K\propto v^2$

Given : $v_1=v$ and $v_2=4v$

Thus ratio of kinetic energy $\frac{K_1}{K_2}=\frac{v_1^2}{v_2^2}$

$\therefore$ $\frac{K_1}{K_2}=\frac{v^2}{(4v{)}^2}=\frac{1}{16}$