Two bodies have masses in the ratio 3:1. They experience forces which impart to them acceleration in the ratio 2:9 respectively. Find the ratio of forces th...

Two bodies have masses in the ratio 3:1. They experience forces which impart to them acceleration in the ratio 2:9 respectively. Find the ratio of forces the masses experienced.

Answer Details

The ratio of forces acting on two bodies is equal to the ratio of their masses multiplied by the ratio of their accelerations. Let's denote the masses of the two bodies as 3m and m, where m is a constant of proportionality. We are given that the accelerations of the two bodies are in the ratio 2:9, which means that the acceleration of the first body is 2a and the acceleration of the second body is 9a, where a is a constant of proportionality. Using Newton's second law of motion, we know that force is equal to mass times acceleration. So, the force experienced by the first body is (3m)(2a) = 6ma, and the force experienced by the second body is (m)(9a) = 9ma. Therefore, the ratio of forces experienced by the two bodies is: 6ma : 9ma Simplifying this ratio by dividing both terms by 3m gives: 2a : 3a Which further simplifies to: 2:3 Therefore, the ratio of forces experienced by the two bodies is 2:3. So, the correct option is "2 : 3".