Question

A rope of length $L$ and mass $M$ is hanging from a right support. The tension in the rope at a distance $x$ from the rigid support is (a) $\mathrm{Mg}$ (b) $\left(\frac{L-x}{L}\right) M g$ (c) $\left(\frac{L}{L-x}\right) \mathrm{Mg}$ (d) $\frac{x}{L} M g$

Name: Problem 76, Chapter 6: Master Resource Book in JEE Main Physics
Uploaded: 2021-09-27T13:53:17-08:00
Duration: 2 min 38 s
Channel: Ajay Singhal
Description: A rope of length L and mass M is hanging from a right support. The tension in the rope at a distance x from the rigid support is (a) Mg (b) ((L-x)/(L)) M g (c) ((L)/(L-x)) Mg (d) (x)/(L) M g

   A rope of length $L$ and mass $M$ is hanging from a right support. The tension in the rope at a distance $x$ from the rigid support is
(a) $\mathrm{Mg}$
(b) $\left(\frac{L-x}{L}\right) M g$
(c) $\left(\frac{L}{L-x}\right) \mathrm{Mg}$
(d) $\frac{x}{L} M g$

Master Resource Book in JEE Main Physics

D. B. Singh 1st Edition

Chapter 6, Problem 76

Instant Answer

Solved by Expert Ajay Singhal

09/27/2021

Step 1

Consider a small segment of the rope at a distance x from the rigid support. Let the length of this segment be dx. Show more…

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A rope of length $L$ and mass $M$ is hanging from a right support. The tension in the rope at a distance $x$ from the rigid support is (a) $\mathrm{Mg}$ (b) $\left(\frac{L-x}{L}\right) M g$ (c) $\left(\frac{L}{L-x}\right) \mathrm{Mg}$ (d) $\frac{x}{L} M g$

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Key Concepts

Static Equilibrium

In a static system, the net force on every element of the system must be zero. For a hanging rope, this principle ensures that the upward tension force at any point exactly balances the downward gravitational force from the portion of the rope hanging below that point.

Linear Mass Density

This concept represents the mass per unit length of an object. For a rope with uniform mass distribution, it is calculated as the total mass divided by its length. This measure is essential for determining the weight of any segment of the rope, which in turn affects the tension in the rope.

Tension Variation in a Distributed Mass

In a rope with mass, tension is not constant but varies along its length. At any given point, the tension is equal to the weight of the rope that lies below that point. This understanding allows us to model and calculate the variable tension in systems where the mass is continuously distributed along the length.

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