Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 7: Problem 861

The temperature of a wire of length 1 meter and area of cross-sectional section \(1 \mathrm{~cm}^{2}\) is increased from \(0^{\circ}\) to $100^{\circ} \mathrm{C}$. If the rod is not allowed to increase in length. What will be the force required ? $\left[\alpha=10^{-5} /{ }^{\circ} \mathrm{C}, \mathrm{Y}=10^{11}\left(\mathrm{~N} / \mathrm{m}^{2}\right)\right]$ (A) \(10^{3} \mathrm{~N}\) (B) \(10^{4} \mathrm{~N}\) (C) \(10^{5} \mathrm{~N}\) (D) \(10^{9} \mathrm{~N}\)

Short Answer

Expert verified
The force required to prevent the wire from expanding is \(10^{4} N\). So, the correct answer is (B).

Step by step solution

01

1. Convert area to the proper unit

Since the given area is in cm², we need to convert it to m²: Area = 1 cm² = 0.0001 m²
02

2. Calculate the change in length of the wire

Using the linear expansion formula, we can calculate the change in length: ΔL = α * L * ΔT Where: α = 10⁻⁵ /°C (coefficient of linear expansion) L = 1 m (initial length of the wire) ΔT = 100 °C (change in temperature) ΔL = (10⁻⁵ /°C)(1 m)(100 °C) = 0.001 m
03

3. Calculate the extension (strain) of the wire

Strain is the ratio of the change in length to the original length: Strain = ΔL / L Strain = 0.001 m / 1 m = 0.001
04

4. Use Young's modulus to find the stress

Now we can use the formula for Young's modulus: Y = stress / strain Where Y is the Young's modulus and is given as 10¹¹ N/m². We can rearrange the formula to find the stress: Stress = Y * strain Stress = (10¹¹ N/m²)(0.001) = 10⁸ N/m²
05

5. Find the force required to prevent the wire from expanding

Now we have the stress, we can find the force using the formula: Force = Stress * Area Force = (10⁸ N/m²)(0.0001 m²) = 10⁴ N The force required to prevent the wire from expanding is 10⁴ N. So, the correct answer is (B).

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.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

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

A body floats in water with one-third of its volume above the surface of water. It is placed in oil it floats with half of: Its volume above the surface of the oil. The specific gravity of the oil is. (A) \((5 / 3)\) (B) \((4 / 3)\) (C) \((3 / 2)\) (D) 1

The temperature at which the vapour pressure of a liquid becomes equals of the external pressure is its. (A) Melting point (B) sublimation point (C) Critical temperature (D) Boiling point

Melting point of ice (A) Increases with increasing pressure (B) Decreases with increasing pressure (C) Is independent of pressure (D) is proportional of pressure

Assertion and Reason: Read the assertion and reason carefully to mark the correct option out of the option given below (A) If both assertion and reason are true and reason is the correct explanation of the assertion. (B) If both assertion and reason are true but reason is not the correct explanation of the assertion. (C) If assertion is true but reason is false. (D) If assertion and reason both are false. Assertion: Young's modulus for a perfectly plastic body is zero. Reason: For a perfectly plastic body restoring force is zero. (A) a (B) \(b\) (C) \(\mathrm{c}\) (D) d

Which is the dimensional formula for modulus of rigidity? (A) \(\mathrm{M}_{1} \mathrm{~L}^{1} \mathrm{~T}^{-2}\) (B) \(\mathrm{M}^{1} \mathrm{~L}^{-1} \mathrm{~T}^{-2}\) (C) \(\mathrm{M}^{1} \mathrm{~L}^{-2} \mathrm{~T}^{-1}\) (D) \(\mathrm{M}^{1} \mathrm{~L}^{-2} \mathrm{~T}^{-2}\)
See all solutions

Recommended explanations on English Textbooks

History of English Language

Read Explanation

Semiotics

Read Explanation

English Grammar Summary

Read Explanation

Discourse

Read Explanation

Key Concepts in Language and Linguistics

Read Explanation

Language Analysis

Read Explanation
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.

Sign-up for free