Question

A 50 kg person stands on a 25 kg platform. He pulls on a rope which is attached to the platform via the frictionless pulleys as shown in the figure. The platform moves upwards at a steady rate. Then the force with which the person pulls the rope is –
        

A) 500N
B) 250N
C) 25N
D) None

Answer 1

Hint: We need to find the force with which the man pulls the rope for the given situation. We should understand that the tension on the rope on which the man pulls has the same force at which he pulls it. So, we need to evaluate the tension on the rope.

Complete answer:
We know that the platform on which the person stands interconnected by ropes and pulley systems. A person pulling the rope via the pulleys has a direct effect on the platform. The platform can rise as shown below.
                            

The normal reaction of the man is in the upward direction and that of the platform is in the downward. The weight of both the person and the platform is downward. We can also see that the tension on the string is in the same direction as that of the normal reaction of the person. The tension on the rope through the pulley attached to the platform has a double effect of the tension on the string being pulled by the person.
Now, let us consider all the above statements mathematically.
\[\begin{align}
  & T+N=Mg\text{ --(1)} \\
 & \text{and,} \\
 & 2T=N+mg\text{ --(2)} \\
\end{align}\]
Adding (1) and (2), we get –
\[\begin{align}
  & 3T=(M+m)g \\
 & \Rightarrow T=\dfrac{(M+m)g}{3} \\
\end{align}\]
Now, we can substitute the given values of masses to get the tension on the string as –
\[\begin{align}
  & T=\dfrac{(M+m)g}{3} \\
 & \Rightarrow T=\dfrac{(50+25)}{3}(10) \\
 & \therefore T=250N \\
\end{align}\]
The force applied by the person on the rope is 250N.

The correct answer is option B.

Note:
The normal reaction of the platform when pulled upwards is directly in the downwards direction which is to be taken care of in this question. The normal reaction is the reaction force due to weight of an object at rest and changes when the object is lifted against gravity.