Question

Two guns $A$ and $B$ can fire bullets at speeds $1\text{km/s}$ and $2\text{km/s}$ respectively, they are fired in all possible directions. The ratio of maximum areas covered by the bullets fired by the two guns, on the ground is:

• A. $1:16$
• B. $1:2$
• C. $1:4$
• D. $1:8$

Answer 1

The correct option is A $1:16$

As we know,

Range, $R_{max}=\frac{u^2}{g}$

and, area $A=\pi R^2$

$\therefore A\propto R^2\text{or}A\propto u^4$
$\therefore \frac{A_1}{A_2}=\frac{u_1^4}{u_2^4}={\left[\frac{1}{2}\right]}^4=\frac{1}{16}$

Hence, $\left(A\right)$ is the correct answer.