Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 7: Problem 1001

The radii of two soap bubbles are \(\mathrm{r}_{1}\) and \(\mathrm{r}_{2} .\) In isothermal conditions two meet together is vacuum Then the radius of the resultant bubble is given by (A) \(\mathrm{R}=\left[\left(\mathrm{r}_{1}+\mathrm{r}_{2}\right) / 2\right]\) (B) \(\mathrm{R}=\mathrm{r}_{1}\left(\mathrm{r}_{1}+\mathrm{r}_{2}+\mathrm{r}_{3}\right)\) (C) \(\mathrm{R}^{2}=\mathrm{r}_{1}^{2}+\mathrm{r}_{2}^{2}\) (D) \(\mathrm{R}=\mathrm{r}_{1}+\mathrm{r}_{2}\)

Short Answer

Expert verified
The radius of the resultant soap bubble is given by the formula \(R = \sqrt{r_1^2 + r_2^2}\). The correct answer is (C) \(R^2 = r_1^2 + r_2^2\).

Step by step solution

01

Given information

We are given the radii of two soap bubbles, \(r_1\) and \(r_2\), and need to find the radius of the resultant soap bubble, R, when they merge. Step 2: Understand the concept of surface area conservation
02

Surface area conservation

Under isothermal conditions and in a vacuum, the surface area of the two soap bubbles (assuming they are spherical) will be conserved during the merging process. The surface area of a soap bubble is given by the formula: \(A = 4\pi r^2\) Step 3: Write the equation for the conservation of surface area
03

Conservation of surface area equation

Using the surface area formula, we can set up the equation for the conservation of surface area: \(A_1 + A_2 = A_R\) Substituting the respective radii and the surface area formula, we get: \(4\pi r_1^2 + 4\pi r_2^2 = 4\pi R^2\) Step 4: Simplify and solve for R
04

Solve for R

Now, we need to solve for R. First, simplify the equation by dividing both sides by \(4\pi\): \(r_1^2 + r_2^2 = R^2\) Now, take the square root of both sides of the equation: \(\sqrt{r_1^2 + r_2^2} = R\) The radius of the resultant soap bubble, R, is given by the formula: \(R = \sqrt{r_1^2 + r_2^2}\) Comparing with the given options, the correct answer is: (C) \(R^2 = r_1^2 + r_2^2\)

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

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 the reason is the correct explanation of the reason. (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 the assertion and reason both are false. (e) If assertion is false but reason is true. Assertion: Fahrenheit is the smallest unit measuring temperature. Reason: Fahrenheit was the first temperature scale used for measuring temperature. (A) \(a\) (B) b (C) \(c\) (D) d (E) e

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

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) \(10^{9} \mathrm{~Pa}\)

What is the relationship between Young's modulus Y, Bulk modulus \(\mathrm{k}\) and modulus of rigidity \(\eta\) ? (A) \(\mathrm{Y}=[9 \eta \mathrm{k} /(\eta+3 \mathrm{k})]\) (B) \(\mathrm{Y}=[9 \mathrm{Yk} /(\mathrm{y}+3 \mathrm{k})]\) (C) \(\mathrm{Y}=[9 \eta \mathrm{k} /(3+\mathrm{k})]\) (D) \(\mathrm{Y}=[3 \eta \mathrm{k} /(9 \eta+\mathrm{k})]\)

Amount of heat required to raise the temperature of a body through $1 \mathrm{k}$ is called it is (A) Water equivalent (B) Thermal capacity (C) Entropy (D) Specific heat
See all solutions

Recommended explanations on English Textbooks

Language Analysis

Read Explanation

International English

Read Explanation

Text Comparison

Read Explanation

Textual Analysis

Read Explanation

Linguistic Terms

Read Explanation

Prosody

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