Two persons A and B perform same amount of work in moving a body through a certain distance d with application of forces acting at angle 45° and 60° with the direction of displacement respectively. The ratio of force applied by person A to the force applied by person B is 1/√x. The value of x is .................... .

Solution

Physics sir · 3 steps

Same work, same distance, so the force along the displacement, F cos θ, must be the same for both.

1. Work by a force. Only the part of the force along the displacement does work, so W = Fd cos θ. Both persons do the same work over the same distance d.

   F_A d cos 45° = F_B d cos 60°

2. Take the ratio. Cancel d to get F_A/F_B = (cos 60°)/(cos 45°) = (1/2)/(1/√2) = √2/2 = 1/√2.
3. So. Comparing 1/√2 with 1/√x gives x = 2.

The common slip: 0.5. Writing F_A/F_B = (cos 45°)/(cos 60°) = √2 flips the ratio and gives x = 1/2, not 2.

The idea to keep. When the work is the same, the larger the angle with the displacement, the larger the force you need, because only F cos θ counts. The force ratio is the inverse of the cosine ratio.

Answer from the NTA final answer key. Solution by PrepWiser.