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A uniform rope of length 5m is on a smooth horizontal surface. It is being pulled by a horizontal force of 20 N at one end. The ratio of tension at a distance of 2m from force end to tension at a distance of 2m from free end is,

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3 : 2

2 : 3

1 : 1

1 : 2

answer is D.

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Detailed Solution

a = Acceleration of the rope = F/m

$F - T_{Q} = (\frac{m}{5} \times 2) \times a \Rightarrow T_{Q} = \frac{3 F}{5}$

$T_{P} = (\frac{m}{5} \times 2) \times a = \frac{2 m}{5} a = \frac{2 m}{5} \times \frac{F}{m} = \frac{2 F}{5}$

$∴ \frac{T_{Q}}{T_{P}} = \frac{3}{2}$

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