Question

Two guns P and Q can fire bullets at speeds 2 km/s and 4 km/s, respectively. From a point on a horizontal ground, they are fired in all possible directions. The ratio of maximum or areas covered by the bullets fired by the two guns, on the ground is

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

Hint:

When comparing the areas covered by objects moving with different speeds, use the square of their speeds as the ratio of the areas.

Answer 1

The Correct Option is D

The area covered by the bullets fired by each gun is proportional to the square of the speed of the bullets. For gun P, the area is proportional to \( v_P^2 \), and for gun Q, it is proportional to \( v_Q^2 \). The ratio of areas is: \[ \frac{\text{Area for gun P}}{\text{Area for gun Q}} = \frac{v_P^2}{v_Q^2} = \frac{(2)^2}{(4)^2} = \frac{1}{16} \] Thus, the correct answer is (D).