Q 11-03-153JEE MainJEE Main 2019 (10 Jan, Shift 1)Easy
Two guns $A$ and $B$ can fire bullets at speeds $1\ \text{km/s}$ and $2\ \text{km/s}$ respectively. From a point on a horizontal ground, 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:
Answer: (A) $1:16$
The bullets land inside a circle whose radius is the maximum range $R = \dfrac{u^2}{g}$. The area is $\pi R^2 \propto u^4$:
$$\frac{A_A}{A_B} = \left(\frac12\right)^4 = \frac1{16}$$
Solution by Sreeraj P, M.Sc Physics