NEET Exam > NEET Questions > Infinite number of bodies, each of mass 2 kg ...
Start Learning for Free
Infinite number of bodies, each of mass 2 kg are situated on x-axis at distances 1m, 2m, 4m, 8m, … ,
respectively, from the origin. The resulting gravitational potential due to this system at the origin will be -
respectively, from the origin. The resulting gravitational potential due to this system at the origin will be -
- a)-G
- b)-8/3G
- c)-4/3 G
- d)-4G
Correct answer is option 'D'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
Infinite number of bodies, each of mass 2 kg are situated on x-axis at...
Most Upvoted Answer
Infinite number of bodies, each of mass 2 kg are situated on x-axis at...
And so on from the origin. Find the gravitational potential at a point P on the x-axis, where P is at a distance of 3 meters from the origin.
Solution:
Let G be the universal gravitational constant, and let M be the mass of each body. Then the gravitational potential at point P due to all the bodies can be found by summing the contributions from each body:
V = -GM(1/1 + 1/2 + 1/4 + 1/8 + ...)
This is an infinite series, but we can simplify it using the formula for a geometric series:
1 + r + r^2 + r^3 + ... = 1/(1-r)
where r is the common ratio. In this case, the common ratio is 1/2, so we have:
1/1 + 1/2 + 1/4 + 1/8 + ... = 1/(1-1/2) = 2
Therefore, the gravitational potential at point P is given by:
V = -GM(2) = -2GM
Substituting the numerical values, we get:
V = -(6.67 x 10^-11 N m^2/kg^2)(2 kg)(2) = -2.22 x 10^-10 J/kg
Note that the gravitational potential is negative, indicating that work must be done to bring a mass from infinity to point P against the gravitational force.
Solution:
Let G be the universal gravitational constant, and let M be the mass of each body. Then the gravitational potential at point P due to all the bodies can be found by summing the contributions from each body:
V = -GM(1/1 + 1/2 + 1/4 + 1/8 + ...)
This is an infinite series, but we can simplify it using the formula for a geometric series:
1 + r + r^2 + r^3 + ... = 1/(1-r)
where r is the common ratio. In this case, the common ratio is 1/2, so we have:
1/1 + 1/2 + 1/4 + 1/8 + ... = 1/(1-1/2) = 2
Therefore, the gravitational potential at point P is given by:
V = -GM(2) = -2GM
Substituting the numerical values, we get:
V = -(6.67 x 10^-11 N m^2/kg^2)(2 kg)(2) = -2.22 x 10^-10 J/kg
Note that the gravitational potential is negative, indicating that work must be done to bring a mass from infinity to point P against the gravitational force.
Attention NEET Students!
To make sure you are not studying endlessly, EduRev has designed NEET study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in NEET.
|
Explore Courses for NEET exam
|
|
Similar NEET Doubts
Top Courses for NEETView all
Infinite number of bodies, each of mass 2 kg are situated on x-axis at distances 1m, 2m, 4m, 8m, … ,respectively, from the origin. The resulting gravitational potential due to this system at the origin will be -a)-Gb)-8/3Gc)-4/3 Gd)-4GCorrect answer is option 'D'. Can you explain this answer?
Question Description
Infinite number of bodies, each of mass 2 kg are situated on x-axis at distances 1m, 2m, 4m, 8m, … ,respectively, from the origin. The resulting gravitational potential due to this system at the origin will be -a)-Gb)-8/3Gc)-4/3 Gd)-4GCorrect answer is option 'D'. Can you explain this answer? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about Infinite number of bodies, each of mass 2 kg are situated on x-axis at distances 1m, 2m, 4m, 8m, … ,respectively, from the origin. The resulting gravitational potential due to this system at the origin will be -a)-Gb)-8/3Gc)-4/3 Gd)-4GCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Infinite number of bodies, each of mass 2 kg are situated on x-axis at distances 1m, 2m, 4m, 8m, … ,respectively, from the origin. The resulting gravitational potential due to this system at the origin will be -a)-Gb)-8/3Gc)-4/3 Gd)-4GCorrect answer is option 'D'. Can you explain this answer?.
Infinite number of bodies, each of mass 2 kg are situated on x-axis at distances 1m, 2m, 4m, 8m, … ,respectively, from the origin. The resulting gravitational potential due to this system at the origin will be -a)-Gb)-8/3Gc)-4/3 Gd)-4GCorrect answer is option 'D'. Can you explain this answer? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about Infinite number of bodies, each of mass 2 kg are situated on x-axis at distances 1m, 2m, 4m, 8m, … ,respectively, from the origin. The resulting gravitational potential due to this system at the origin will be -a)-Gb)-8/3Gc)-4/3 Gd)-4GCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Infinite number of bodies, each of mass 2 kg are situated on x-axis at distances 1m, 2m, 4m, 8m, … ,respectively, from the origin. The resulting gravitational potential due to this system at the origin will be -a)-Gb)-8/3Gc)-4/3 Gd)-4GCorrect answer is option 'D'. Can you explain this answer?.
Solutions for Infinite number of bodies, each of mass 2 kg are situated on x-axis at distances 1m, 2m, 4m, 8m, … ,respectively, from the origin. The resulting gravitational potential due to this system at the origin will be -a)-Gb)-8/3Gc)-4/3 Gd)-4GCorrect answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for NEET.
Download more important topics, notes, lectures and mock test series for NEET Exam by signing up for free.
Here you can find the meaning of Infinite number of bodies, each of mass 2 kg are situated on x-axis at distances 1m, 2m, 4m, 8m, … ,respectively, from the origin. The resulting gravitational potential due to this system at the origin will be -a)-Gb)-8/3Gc)-4/3 Gd)-4GCorrect answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
Infinite number of bodies, each of mass 2 kg are situated on x-axis at distances 1m, 2m, 4m, 8m, … ,respectively, from the origin. The resulting gravitational potential due to this system at the origin will be -a)-Gb)-8/3Gc)-4/3 Gd)-4GCorrect answer is option 'D'. Can you explain this answer?, a detailed solution for Infinite number of bodies, each of mass 2 kg are situated on x-axis at distances 1m, 2m, 4m, 8m, … ,respectively, from the origin. The resulting gravitational potential due to this system at the origin will be -a)-Gb)-8/3Gc)-4/3 Gd)-4GCorrect answer is option 'D'. Can you explain this answer? has been provided alongside types of Infinite number of bodies, each of mass 2 kg are situated on x-axis at distances 1m, 2m, 4m, 8m, … ,respectively, from the origin. The resulting gravitational potential due to this system at the origin will be -a)-Gb)-8/3Gc)-4/3 Gd)-4GCorrect answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Infinite number of bodies, each of mass 2 kg are situated on x-axis at distances 1m, 2m, 4m, 8m, … ,respectively, from the origin. The resulting gravitational potential due to this system at the origin will be -a)-Gb)-8/3Gc)-4/3 Gd)-4GCorrect answer is option 'D'. Can you explain this answer? tests, examples and also practice NEET tests.
|
|
Explore Courses for NEET exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup