/*! 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 44 The ratio of maximum and minimum... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 44

The ratio of maximum and minimum magnitudes of the resultant of two vectors \(\vec{a}\) and \(\vec{b}\) is \(3: 1\). Now \(|\vec{a}|\) is equal to (A) \(|\vec{b}|\) (B) \(2|\vec{b}|\) (C) \(3|\vec{b}|\) (D) \(4|\vec{b}|\)

Short Answer

Expert verified
The short answer to the question is (B) \(2|\vec{b}|\), derived from the equation \(|\vec{a}| = 2|\vec{b}|\).

Step by step solution

01

Find the maximum magnitude of the resultant vector

When two vectors are parallel, their magnitudes add up. Thus, the maximum magnitude of the resultant vector, \(|\vec{R}_{max}|\), can be found by adding the magnitudes of vectors \(\vec{a}\) and \(\vec{b}\): \[|\vec{R}_{max}| = |\vec{a}| + |\vec{b}|\]
02

Find the minimum magnitude of the resultant vector

When two vectors are anti-parallel, their magnitudes subtract from each other. Thus, the minimum magnitude of the resultant vector, \(|\vec{R}_{min}|\), can be found by taking the difference between the magnitudes of vectors \(\vec{a}\) and \(\vec{b}\): \[|\vec{R}_{min}| = |\vec{a}| - |\vec{b}|\]
03

Use the given ratio to find the relationship between the magnitudes of \(\vec{a}\) and \(\vec{b}\)

We are given that the ratio of the maximum and the minimum magnitudes of the resultant vector is \(3:1\). Therefore, we can write: \[\frac{|\vec{R}_{max}|}{|\vec{R}_{min}|} = \frac{3}{1}\] Substituting the expressions from steps 1 and 2, we get: \[\frac{|\vec{a}| + |\vec{b}|}{|\vec{a}| - |\vec{b}|} = 3\]
04

Solve for the relationship between the magnitudes of \(\vec{a}\) and \(\vec{b}\)

Cross multiplying the equation we found in step 3, we get: \[(|\vec{a}| + |\vec{b}|)(1) = (|\vec{a}| - |\vec{b}|)(3)\] Expanding both sides, we get: \[|\vec{a}| + |\vec{b}| = 3|\vec{a}| - 3|\vec{b}|\] Now, simplify and solve for \(|\vec{a}|\): \[-2|\vec{a}| = -4|\vec{b}|\] \[|\vec{a}| = 2|\vec{b}|\] Since \(|\vec{a}| = 2|\vec{b}|\), the correct answer is (B) \(2|\vec{b}|\).

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.

Over 30 million students worldwide already upgrade their learning with 91影视!

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

Mark the correct statement (A) \(|\vec{a}+\vec{b}| \geq|\vec{a}|+|\vec{b}|\) (B) \(|\vec{a}+\vec{b}| \leq|\vec{a}|+|\vec{b}|\) (C) \(|\vec{a}-\vec{b}| \geq|\vec{a}|+|\vec{b}|\) (D) All of the above

The least count of a stop watch is \(1 / 5 \mathrm{~s}\). The time of 20 oscillations of a pendulum is measured to be \(25 \mathrm{~s}\). The minimum percentage error in the measurement of time will be (A) \(0.1 \%\) (B) \(0.8 \%\) (C) \(1.8 \%\) (D) \(8 \%\)

The dimensional formula of magnetic flux is (A) \(\left[M L^{2} T^{-2} A^{-1}\right]\) (B) \(\left[M L^{0} T^{-2} A^{-2}\right]\) (C) \(\left[M^{0} L^{-2} T^{-2} A^{-2}\right]\) (D) \(\left[M L^{2} T^{-1} A^{3}\right]\)

Electrons in a TV tube move horizontally South to North. Vertical component of earth's magnetic field points down. The electron is deflected towards (A) West (B) No deflection (C) East (D) North to South

The length, width and thickness of a block are (100.0 \(\pm 0.1) \mathrm{cm},(10.00 \pm 0.01) \mathrm{cm}\) and \((1.000 \pm 0.001) \mathrm{cm}\) respectively. The maximum possible error in its volume will be (A) \(\pm 0.111 \mathrm{~cm}^{3}\) (B) \(\pm 0.012 \mathrm{~cm}^{3}\) (C) \(+0.03 \mathrm{~cm}^{3}\) (D) None of these
See all solutions

Recommended explanations on Physics Textbooks

Famous Physicists

Read Explanation

Fields in Physics

Read Explanation

Torque and Rotational Motion

Read Explanation

Electric Charge Field and Potential

Read Explanation

Force

Read Explanation

Linear Momentum

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.