Question

Two bodies which are equal in mass, move with uniform velocities of $6m{s}^{-1}$ and $18m{s}^{-1}$, respectively. Find the ratio of their kinetic energies.

Answer 1

Step 1 : Given,

Since the mass of both the bodies is equal, let their masses be $m$.

Velocity of the first body $v_1=6m{s}^{-1}$

And that of second body $v_2=8m{s}^{-1}$

Step 2 : Ratio of their kinetic energies,

$\frac{K.E{{.}_1}^{}}{K.E{.}_2}=\frac{{\displaystyle \frac{1}{2}}m{v_1}^2}{{\displaystyle \frac{1}{2}}m{v_2}^2}$

$\frac{K.E{.}_1}{K.E{.}_2}=\frac{{v_1}^2}{{v_2}^2}$

$\frac{K.E{.}_1}{K.E{.}_2}=\frac{6^2}{{18}^2}=\frac{36}{324}=\frac{1}{9}$

Hence the ratio is $1:9$.