A boy of mass 40 kg stands in a frame of mass 360 kg. He pulls on a light rope which passes over a pulley. The other end of the rope is firmly attached to the frame. What force should be exerted by the boy on the rope for the system to be in equilibrium?

Options

A. 40g
B. 400g
C. 200g
D. 100g

Answer

C

Explanation

If T is the tension in the rope, then the force exerted by the boy B on the rope is equal to the force exerted by the rope on the boy. Let R be the normal reaction between the boy and the frame.
The free body diagrams of boy and frame are shown in figures (a) and (b) respectively.

From the free body diagram of boy
`T+ R = 40 g `
From the free body diagram of frame
`T=R + 360 g `
Adding (i) and (ii), we get
`2T = 400 g or T = 200 g `