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One end of a light rope is tied directly to the ceiling. A man of mass m initially at rest on the ground starts climbing (slowly) the rope without slipping upto a height ℓ which is quite large in comparison to the dimension of man. From the time he starts at rest on the ground to the time he is hanging at rest at a height ℓ . Then A) work done on man by rope is zero. B) work done by gravity is –mg ℓ C) work done by man is mg ℓ D) work done by man is zero.

One end of a light rope is tied directly to the ceiling. A man of mass m initially at rest on the ground starts climbing (slowly) the rope without slipping upto a height ℓ which is quite large in comparison to the dimension of man. From the time he starts at rest on the ground to the time he is hanging at rest at a height ℓ . Then
A) work done on man by rope is zero.  B) work done by gravity is –mg ℓ  C) work done by man is mg ℓ  D) work done by man is zero.

Grade:12

2 Answers

Piyush Kumar Behera
417 Points
4 years ago
As the man is moving upwards slowly.Hence the net force on the man can be assumed to be zero.
So there are only two forces, gravitational and tension force of the rope acting on the man.
Hence man applies no force.”Dont go practically,think analytically”,Hence work done by man is zero.
Gravitational force = tension = mg.
As the displacement is upwards hence the work done by gravitational force is negative and equals to -mgl.
 
As the displacement is upwards hence the work done by tension force is positive and equals to mgl.
 
Hence the answer to the above question is B and D
I hope it helps!!
Chirag Mehta
9 Points
3 years ago
answer A,B,C
rope applies a force on man(friction) at the point of contact(his hand) , his hand remains stationary wrt ground, so does the rope. 
dW= F.dx . dx(small displeacement) of rope or man’s hand is 0. 
therefore work done by man on rope is 0. and so is the work done by rope on man.
however, man does some work against gravity, because rest of his joints move in order to pull himself up, after which he removes his hand and holds a upper portion of rope.
work done against gravity = -mgl,
work done by man=mgl

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