question_answer

Two guns A and B can fire bullets at speeds 1 km/s and 2 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- [JEE Main 10-Jan-2019 Morning]

A) 1 : 16

B) 1 : 8

C) 1 : 2

D) 1 : 4

Correct Answer: A

Solution :

[a]

Area covered \[=\text{ }\pi \,{{R}^{2}}\]

When R is maximum area covered is also maximum

\[R\,=\,\frac{{{u}^{2}}\,\sin \,2\,\theta }{g}\]

\[{{R}_{\max }}\,=\,\frac{{{u}^{2}}\,}{g}\,(\theta \,\,=\,\,45{}^\circ )\]

Area covered \[\propto {{u}^{4}}\]

Ratio \[=\,{{\left( \frac{1}{2} \right)}^{4}}\,=\,\frac{1}{16}\]