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Question

A 50 kg person stands on a 25 kg platform. He pulls the rope which is attached to the platform through the frictionless pulleys as shown in the figure. If the platform moves upwards at a steady velocity, find the force with which man pulls the rope. Take g=10 m/s2.


  1. 325 N
  2. 175 N
  3. 250 N
  4. 750 N


Solution

The correct option is C 250 N
Let the tension in the rope be T everywhere throughout the length of the string. So, the tension in the string connecting the platform to the adjacent pulley will be 2T as pulley and string are massless.

Steady velocity means, for the system of (platform+man):
a=dvdt=0 ...(i)

From the FBD of system of (platform+man), applying the equilibrium condition in vertical direction as dictated by Eq. (i):
2T+T=(25+50)g
T=7503=250 N

At the point where the man is holding the string, T is acting upwards on him, so by Newton's 3rd law, he must have pulled the rope downwards by a force, T=250 N.

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