Question

Two formula cars in a race have the same mass but their kinetic energies are different. The ratio of their kinetic energies is 1:16. What would be the corresponding ratio of their velocities?

• A. $1:2$
• B. $4:1$
• C. $2:1$
• D. $1:4$

Answer 1

The correct option is D $1:4$

$K.E.=\frac{1}{2}$$m{v}^2$,
where $m$ is the mass of the object and
$v$ is the velocity of the object.
Given, $\frac{{KE}_1}{{KE}_2}=1:16$
where $K{E}_1$ is the kinetic energy of the first car and $K{E}_2$ is the kinetic energy of the other car.

$\Rightarrow \frac{K{E}_1}{K{E}_2}=\frac{\frac{1}{2}m{v_1}^2}{\frac{1}{2}m{v_2}^2}=\frac{v_1^2}{v_2^2}=\frac{1}{16}$

$\Rightarrow \frac{v_1}{v_2}=\frac{1}{4}$

So, the ratio of velocities will be $1:4$.