In the given diagram, with what force must the man pull the rope to hold the plank in position? The weight of the man is 60 x 9.81 N. Neglect the weights of the plank, rope, and pulley.

Explanation

This is the following solution: We are given a system in which a man is standing on a plank which is attached to two pulleys through ropes as shown in the figure. The man is pulling the end of a rope that is attached to the pulley 2 so that the whole system will be at rest. We can understand that since the weights of the pulleys, ropes, and the plank are to be neglected, the only force that needs to be balanced is the weight due to the man's mass on the plank in the downward direction. i.e., F total=0 Let us consider the man on the plank and the tension on the rope on pulley 2 due to the force he exerts as - T+N=mg ∴T+N−mg=0 --(1) Now, let us consider the normal reaction of the plank and the tensions on the ropes connected to pulleys 1 and 2 as - 2T+T=N ∴3T−N=0 --(2) Let us substitute (1) in (2) to the value for the normal reaction as - 3T−N=0 ⇒3(mg−N)−N=0 ∴N=3/4mg Now, we can substitute the above relation in (1) to get the tension on the rope which will give the necessary force as - T+N−mg=0 ⇒T+(3/4mg−mg)=0 ⇒T=1/4mg ⇒T=1/4(60)kg×g ∴T=15kg×g= 15×9.81 N This is the required force to be exerted by the man to keep the plank in position. The correct answer is option A.