/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 9 An elastic metal rod will change... [FREE SOLUTION] | 91Ó°ÊÓ

91Ó°ÊÓ

An elastic metal rod will change its length when it (a) falls vertically under its weight (b) is pulled along its length by a force acting at one end (c) rotates about an axis at one end (d) slides on a rough surface

Short Answer

Expert verified
The rod's length changes in situation (b) because pulling applies a force along its length.

Step by step solution

01

Understanding Elasticity

Elastic materials change their shape or length when a force is applied to them and return to their original shape or length when the force is removed. Therefore, the situations where the shape or length change temporarily due to external forces are important.
02

Evaluating Fall Under Gravity

When the rod falls vertically under its weight (a), it experiences a force due to gravity. However, this force is uniformly distributed throughout the rod, and the length does not change due to this vertical fall alone, as the stress is constant along the rod's length.
03

Evaluating Pulling Force

In scenario (b), when the rod is pulled along its length by a force acting at one end, the force directly stretches the rod. This causes a change in length as the force is applied along the lengthwise axis.
04

Evaluating Rotation

In scenario (c), rotating about an axis at one end does not by itself apply a stretching or compressive force along the length of the rod. Therefore, the rod's length remains unchanged due to rotational motion itself.
05

Evaluating Sliding on Rough Surface

In scenario (d), as the rod slides on a rough surface, the primary forces at play are frictional, which act perpendicular to the length and do not change the rod's length, assuming no stretching or compressive forces are applied parallel to the rod.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91Ó°ÊÓ!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Elastic Deformation
Elastic deformation is when an object changes its shape or size temporarily under an applied force and returns to its original state once the force is removed. Think of it as the object's ability to stretch and then snap back to its initial configuration.
  • Elastic deformation occurs when the applied force is within the elastic limit of the material.
  • It involves reversible changes, meaning the material regains its original dimensions after the force ceases.
  • It's essential in understanding material behavior under load, especially in areas like engineering and material science.
When you pull a rubber band and let it go, it returns to its original length. That's a classic example of elastic deformation. In physics problems, like the one with the metal rod, recognizing instances of elastic deformation helps us predict how objects behave under similar forces.
For instance, when the rod is **pulled** along its length, the stretching caused by the force is a demonstration of elastic deformation. It will resume its original size once the pulling force stops, assuming the force doesn’t exceed the material's elastic limit.
Force and Motion
Force is any interaction that changes the motion of an object. It can cause an object to start moving, stop moving, change direction, or change shape. When combined with motion, it forms the crux of understanding how objects respond under various physical conditions.
  • A force applied on an object can initiate movement or deform the object.
  • Newton's laws of motion describe how forces affect motion.
  • For a rod, being pulled at one end causes it to move if unrestrained, or stretch if held in place.
In the exercise, when the **rod falls vertically**, the force of gravity acts upon it. While this force does not change the rod's length, it sets the body in motion, demonstrating how force influences motion. However, it's only when a **specific directional force**, like a pull, is applied along its length, that the rod experiences both motion and a change in length. This illustrates the complexity of forces in creating motion and deformation.
Mechanical Stress
Mechanical stress is the internal force experienced by a material when an external force is applied to it. Stress is a key concept in determining how materials will react under force.
  • Stress is measured in force per unit area, such as Pascals (Pa) in the SI system.
  • It can cause deformation, depending on the material's properties and the type of stress applied.
  • Common types include tensile stress (stretching) and compressive stress (squeezing).
Tensile stress, for instance, is what occurs in the rod when it is **pulled** by a force at one end. The force stretches the rod, causing the atoms in the material to move apart slightly, resulting in an elongation.
However, during scenarios like a **rotational motion** at one end, the stress distribution does not stretch or compress the rod along its length, which explains why its length remains unchanged. Understanding mechanical stress is crucial for evaluating how different forces influence structural integrity and behavior of materials.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

\(\Lambda\) rectangular container of base dimensions \(2 \mathrm{~m} \times 1 \mathrm{~m}\) and height \(0.5 \mathrm{~m}\) is filled with water upto height of \(0.2 \mathrm{~m}\). 'The mass of the empty container is \(1 \mathrm{~kg}\). The coefficient of friction between conLainer and plane is \(0.5\). The container is placed on the pane inclined at \(45^{\circ}\) to the horizontal. The angle of the water surface to the horizontal is (a) \(\tan ^{\prime}\left(\frac{1}{2}\right)\) (b) \(\tan ^{1} 2\) (c) \(\tan ^{\prime}\left(\frac{1}{3}\right)\) (d) \(\tan ^{1} 3\)

\(\Lambda\) wooden plank of length \(\mathrm{lm}\) and uniform cross-section is hinged at one end to the bottom of the tank. 'Ihe tank is filled with water upto a height of \(0.5 \mathrm{~m}\). 'lhe specific gravity of the plank is \(0.5\). The plank makes an angle of \(45^{\circ}\) with the vertical in the cquilibrium position. \(A\) is the midpoint of the plank. \(B\) is the middle point of the dipped parl of the plank. Which of the following are correct? (a) The weight of the plank acts downwards at \(\Lambda\) (b) The buoyant force acts through \(B\) (c) \(O B-\frac{1}{\sqrt{2}} m\) (d) Both (b) and (c)

Statement-1 : A wooden picce floats hall submerged in a tank of water. I[ the system accelerates up then the wooden piece will remain half submerged. Statement-2: When the system starts accelerating up, then effective \(g\) will be same for both water and wooden piece.

A heavy and uniform rod is hanging frecly vertically from a fixed support. It is strelched by its own weight. Which of the following are correct about the diameter of the stretched rod? (a) It is uniform everywhere (b) It is maximum in the middle (c) It is largest at the top and gradually decreases down the rod (d) It is smallest at the top and gradually increases down the rod

If a sample of metal weighs \(210 \mathrm{gm}\) in air, \(180 \mathrm{gm}\) in watcr and \(120 \mathrm{gm}\) in a liquid; then (a) relative density of metal is 3 (b) relative density of metal is 7 (c) relative density of liquid is 3 (d) relative density of liquid is \(1 / 3\)

See all solutions

Recommended explanations on Physics Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.