Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 7: Problem 973

A rubber ball when taken to the bottom of a \(100 \mathrm{~m}\) deep take decrease in volume by \(1 \%\) Hence, the bulk modulus of rubber is $\ldots \ldots \ldots . . .\left[\mathrm{g}=10\left(\mathrm{~m} / \mathrm{s}^{2}\right)\right]$ (A) \(10^{6} \mathrm{~Pa}\) (B) \(10^{8} \mathrm{~Pa}\) (C) \(10^{7} \mathrm{~Pa}\) (D) \(10^{9} \mathrm{~Pa}\)

Short Answer

Expert verified
The bulk modulus of the rubber ball is \(10^8 \mathrm{~Pa}\).

Step by step solution

01

Find the pressure at the bottom of the tank

First, we need to determine the pressure at the bottom of the tank using the depth and gravity acting on the water. We can do that using the formula: \(P = \rho \cdot g \cdot h\) where: \(P\) is the pressure at the bottom, \(\rho\) is the density of water (approximately \(1000 \mathrm{~kg/m^3}\)), \(g\) is the acceleration due to gravity (\(10 \mathrm{~m/s^2}\)), and \(h\) is the depth (\(100 \mathrm{~m}\)). By substituting the values, we get: \(P = 1000 \cdot 10 \cdot 100\)
02

Calculate the pressure at the bottom of the tank

Now, let's calculate the pressure at the bottom of the tank: \(P = 1000 \cdot 10 \cdot 100 = 10^6 \mathrm{~Pa}\) The pressure at the bottom of the tank is \(10^6 \mathrm{~Pa}\).
03

Calculate the change in volume percentage

We know that the volume of the rubber ball decreases by \(1 \%\) when submerged at the bottom of the tank, which means the change in volume as a fraction is \(0.01\). Let the original volume be \(V\), then the change in volume is \(0.01V\).
04

Use the formula for bulk modulus and solve for it

We can now use the formula for bulk modulus to calculate the bulk modulus of the rubber ball: Bulk Modulus = \(\dfrac{\Delta P}{\dfrac{\Delta V}{V_0}}\) Here, \(\Delta P = 10^6 \mathrm{~Pa}\), and \(\dfrac{\Delta V}{V_0} = 0.01\). Now, we can solve for the bulk modulus: Bulk Modulus = \(\dfrac{10^6}{0.01} = 10^8 \mathrm{~Pa}\) The bulk modulus of the rubber ball is \(10^8 \mathrm{~Pa}\). Therefore, the correct answer is (B) \(10^8 \mathrm{~Pa}\).

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

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: The stretching of a coil is determined by its shear modulus. Reason: Shear modulus change only shape of a body keeping its dimensions unchanged. (A) a (B) \(\mathrm{b}\) (C) \(\mathrm{c}\) (D) \(\mathrm{d}\)

The resistance of a resistance thermometer has values \(2.71\) and $3.70 \mathrm{ohm}\( at \)10^{\circ} \mathrm{C}\( and \)100^{\circ} \mathrm{C}$. The temperature at which the resistance is \(3.26 \mathrm{ohm}\) is (A) \(40^{\circ} \mathrm{C}\) (B) \(50^{\circ} \mathrm{C}\) (C) \(60^{\circ} \mathrm{C}\) (D) \(70^{\circ} \mathrm{C}\)

The bulk modulus of an ideal gas at constant temperature..... (A) is equal to its volume \(\mathrm{V}\) (B) is equal to \(\mathrm{P} / 2\) (C) is equal to its pressure \(\mathrm{P}\) (D) cannot be determined

8000 identical water drops are combined to form a bigdrop. Then the ratio of the final surface energy to the initial surface energy of all the drops together is (A) \(1: 10\) (B) \(1: 15\) (C) \(1: 20\) (D) \(1: 25\)

A square frame of side \(\mathrm{L}\) is dipped in a liquid on taking out a membrance is formed if the surface tension of the liquid is \(\mathrm{T}\), the force acting on the frame will be. (A) \(2 \mathrm{TL}\) (B) \(4 \mathrm{TL}\) (C) \(8 \mathrm{TL}\) (D) \(10 \mathrm{TL}\)
See all solutions

Recommended explanations on English Textbooks

Essay Plan

Read Explanation

Lexis and Semantics Summary

Read Explanation

International English

Read Explanation

Argumentative Essay

Read Explanation

Rhetoric

Read Explanation

Cues and Conventions

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