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Q.

A uniform rope of length L, resting on a frictionless horizontal table is pulled at one end by a force F. What is the tension in the rope at a distance x from the end where the force is applied ?

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a

$F (L - x)$

b

$F (1 - x / L)$

c

$(L - x) / F$

d

$F x / L$

answer is D.

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Detailed Solution

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mass of the length x: $m = \frac{M}{L} x$

mass of the remaining length: $m' = \frac{M}{L} (L - x)$

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

$\Rightarrow T = m' a = \frac{F}{M} \times \frac{M}{L} (L - x) = \frac{F}{L} (L - x)$

$\Rightarrow T = F (1 - \frac{x}{L})$

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A uniform rope of length L, resting on a frictionless horizontal table is pulled at one end by a force F. What is the tension in the rope at a distance x from the end where the force is applied ?