Balls A and B attract each other gravitationally with a force of magnitude F at distance R. If we triple the mass of ball B and triple the separation of the balls to 3R, what is the magnitude of their attractive force now? A. F B. F/3 C. 3F D. F/9 OD OB O C O A
Balls A and B attract each other gravitationally with a force of magnitude F at distance R. If we triple the mass of ball B and triple the separation of the balls to 3R, what is the magnitude of their attractive force now? A. F B. F/3 C. 3F D. F/9 OD OB O C O A
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
Related questions
Topic Video
Question
![**Question:**
Balls A and B attract each other gravitationally with a force of magnitude F at distance R. If we triple the mass of ball B and triple the separation of the balls to 3R, what is the magnitude of their attractive force now?
**Options:**
A. F
B. F/3
C. 3F
D. F/9
**Answer Choices:**
- ○ D
- ○ B
- ○ C
- ○ A
**Explanation:**
Using Newton’s law of universal gravitation, the gravitational force between two masses is given by:
\[ F = \frac{G \cdot m_1 \cdot m_2}{r^2} \]
Where \( G \) is the gravitational constant, \( m_1 \) and \( m_2 \) are the masses, and \( r \) is the distance between their centers.
If the mass of ball B is tripled, it becomes \( 3m_2 \). If the separation is tripled to \( 3R \), the new force \( F' \) is:
\[ F' = \frac{G \cdot m_1 \cdot (3m_2)}{(3R)^2} = \frac{G \cdot m_1 \cdot 3m_2}{9R^2} \]
Thus,
\[ F' = \frac{1}{3} \left(\frac{G \cdot m_1 \cdot m_2}{R^2}\right) = \frac{1}{3}F \]
Therefore, the correct answer is B. F/3.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fab8e90de-1834-4897-8d02-45bfaff51002%2Faddebca7-8de6-4652-98e8-0e0ff4610014%2Fvkl2oqm_processed.png&w=3840&q=75)
Transcribed Image Text:**Question:**
Balls A and B attract each other gravitationally with a force of magnitude F at distance R. If we triple the mass of ball B and triple the separation of the balls to 3R, what is the magnitude of their attractive force now?
**Options:**
A. F
B. F/3
C. 3F
D. F/9
**Answer Choices:**
- ○ D
- ○ B
- ○ C
- ○ A
**Explanation:**
Using Newton’s law of universal gravitation, the gravitational force between two masses is given by:
\[ F = \frac{G \cdot m_1 \cdot m_2}{r^2} \]
Where \( G \) is the gravitational constant, \( m_1 \) and \( m_2 \) are the masses, and \( r \) is the distance between their centers.
If the mass of ball B is tripled, it becomes \( 3m_2 \). If the separation is tripled to \( 3R \), the new force \( F' \) is:
\[ F' = \frac{G \cdot m_1 \cdot (3m_2)}{(3R)^2} = \frac{G \cdot m_1 \cdot 3m_2}{9R^2} \]
Thus,
\[ F' = \frac{1}{3} \left(\frac{G \cdot m_1 \cdot m_2}{R^2}\right) = \frac{1}{3}F \]
Therefore, the correct answer is B. F/3.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.Recommended textbooks for you
College Physics
Physics
ISBN:
9781305952300
Author:
Raymond A. Serway, Chris Vuille
Publisher:
Cengage Learning
University Physics (14th Edition)
Physics
ISBN:
9780133969290
Author:
Hugh D. Young, Roger A. Freedman
Publisher:
PEARSON
Introduction To Quantum Mechanics
Physics
ISBN:
9781107189638
Author:
Griffiths, David J., Schroeter, Darrell F.
Publisher:
Cambridge University Press
College Physics
Physics
ISBN:
9781305952300
Author:
Raymond A. Serway, Chris Vuille
Publisher:
Cengage Learning
University Physics (14th Edition)
Physics
ISBN:
9780133969290
Author:
Hugh D. Young, Roger A. Freedman
Publisher:
PEARSON
Introduction To Quantum Mechanics
Physics
ISBN:
9781107189638
Author:
Griffiths, David J., Schroeter, Darrell F.
Publisher:
Cambridge University Press
Physics for Scientists and Engineers
Physics
ISBN:
9781337553278
Author:
Raymond A. Serway, John W. Jewett
Publisher:
Cengage Learning
Lecture- Tutorials for Introductory Astronomy
Physics
ISBN:
9780321820464
Author:
Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina Brissenden
Publisher:
Addison-Wesley
College Physics: A Strategic Approach (4th Editio…
Physics
ISBN:
9780134609034
Author:
Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field
Publisher:
PEARSON