Question

A gun is firing bullets with velocity $v_0$ by rotating through ${360}^{\circ }$ in the horizontal plane. The maximum area covered by the bullets is

• A. $\frac{\pi v_0^2}{g^2}$
• B. $\frac{{\pi }^2{v}_0^2}{g^2}$
• C. $\frac{{\pi }^2{v}_0^4}{g^2}$
• D. $\frac{\pi v_0^4}{g^2}$

Answer 1

The correct option is D $\frac{\pi v_0^4}{g^2}$

Here the distance covered by the bullet is considered as radius r.
Thus, the maximum range $r=\frac{u^2}{g}=\frac{v_0^2}{g}$.
The maximum area covered by the bullets is $A=\pi r^2=\pi (v_0^2/g{)}^2=\frac{\pi v_0^4}{g^2}$