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A uniform rope of length $10 m$ 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 4m from force end to tension at a distance of 4m from free end is,

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$1 : 2$

$2 : 3$

$1 : 1$

$3 : 2$

answer is D.

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Detailed Solution

From force end : $F - T^{1} = \frac{4 M}{10} a$

From free end : $T = \frac{4 M}{10} a$

Given : $F = 20 N$

$\Rightarrow a = \frac{F}{M}$

So, $F - T^{1} = \frac{4 M}{10} \times \frac{F}{M} = \frac{4 F}{10}$

$\Rightarrow T^{1} = \frac{6 F}{10}$

Also, $T = \frac{4 F}{10}$

Thus, $T^{1} : T = 3 : 2$

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