Question

Two formula one 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. 4:1
• B. 1:4
• C. 2:1
• D. 1:2

Answer 1

The correct option is B

1:4

Kinetic energy of an object,$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.

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

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

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