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Chapter 7: Q. 28 (page 178)

A rope of lengthL and mass m is suspended from the ceiling. Find an expression for the tension in the rope at position y, measured upward from the free end of the rope.

Short Answer

Expert verified

The tension in the rope at positiony, measured upward from the free end is $\frac{m g y}{L}$ .

Step by step solution

01

Given information

Mass of rope is $m$

The length of the rope is $L$

02

Explanation

The weight of the rope is given as

$w = m g$

where m is the mass of the rope suspended from the ceiling.

Weight of the rope per length L $= \frac{m g}{L}$

Weight of the rope at position y $= \frac{m g}{L} \times y$

Tension $T = \frac{m g y}{L}$

The tension in the rope at position y, measured upward from the free end is $\frac{m g y}{L}$

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