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Question

A uniform rope of length L, resting on frictionless horizontal surface is pulled at one end by a force F. Then the tension T in the rope at a distance l from the end where the force F is applied is

A
T=F
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B
T=FLL
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C
T=FIL
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D
T=F(11L)
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Solution

The correct option is D T=F(11L)
Let tension at P be T. Imagine rope to be divided into two parts A and B
Mass of rope=M
Mass of part A=MA=MLI
Mass of part B=MB=ML(LI)
Let the rope move with acceleration a, then for part A
FT=MAa
or FT=MIaL...(i)
For part B TO=MBa
or T=ML(LI)a...(ii)
Adding Eqs (i) and (ii) we get
F=MLa(1+LI)=MLa.L=Maa=FM....(iii)
From Eqs. (i), (ii), (iii)
T=ML(L1).FM=ML(L1)=F(11L)

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