Class 11 Exam > Class 11 Questions > A hollow spherical shell is compressed to hal...
Start Learning for Free
A hollow spherical shell is compressed to half its radius. The gravitational potential at the centre
- a)Increases
- b)Decreases
- c)Remains same
- d)Ruring the compression increases then returns at the previous value
Correct answer is option 'B'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
A hollow spherical shell is compressed to half its radius. The gravita...
Gravitational Potential V = -GM/R for hollow spherical shell at the centre. If we replace R by R/2 then we get V = -2GM/R. Therefore it decreases.
Most Upvoted Answer
A hollow spherical shell is compressed to half its radius. The gravita...
Gravitational potential (v)=-GM/R for hallow spherical shell at the centre.Now multiply and divide -GM/R with R^2. We get v=-gR.(since GM/R^2=g). when radius is reduced to half the gravitational potential =v=-gR/2.Therefore potential decreases
Free Test
FREE
| Start Free Test |
Community Answer
A hollow spherical shell is compressed to half its radius. The gravita...
Explanation:
When a hollow spherical shell is compressed to half its radius, the mass of the shell remains the same. However, the distribution of mass changes, resulting in a different gravitational potential at the center.
Gravitational Potential:
Gravitational potential is the amount of work done in bringing a unit mass from infinity to a point in the gravitational field. It is given by the equation:
V = -GM/r
where V is the gravitational potential, G is the gravitational constant, M is the mass of the object, and r is the distance from the center of the object.
Compressing the Spherical Shell:
When the hollow spherical shell is compressed to half its radius, the mass is concentrated closer to the center. This means that the distance (r) from the center to any point within the shell decreases. As a result, the gravitational potential at the center of the shell changes.
Effect on Gravitational Potential:
Since the mass of the shell remains the same, the only change is in the distance (r). As the radius is halved, r becomes half of its original value. Plugging this new value of r into the gravitational potential equation, we get:
V' = -GM/(r/2) = -2GM/r
Comparing this with the original gravitational potential equation, we can see that the potential at the center has decreased by a factor of 2. Therefore, the correct answer is option 'B': Decreases.
Conclusion:
When a hollow spherical shell is compressed to half its radius, the gravitational potential at the center decreases. This is because the mass remains the same, but the distance from the center to any point within the shell is halved.
When a hollow spherical shell is compressed to half its radius, the mass of the shell remains the same. However, the distribution of mass changes, resulting in a different gravitational potential at the center.
Gravitational Potential:
Gravitational potential is the amount of work done in bringing a unit mass from infinity to a point in the gravitational field. It is given by the equation:
V = -GM/r
where V is the gravitational potential, G is the gravitational constant, M is the mass of the object, and r is the distance from the center of the object.
Compressing the Spherical Shell:
When the hollow spherical shell is compressed to half its radius, the mass is concentrated closer to the center. This means that the distance (r) from the center to any point within the shell decreases. As a result, the gravitational potential at the center of the shell changes.
Effect on Gravitational Potential:
Since the mass of the shell remains the same, the only change is in the distance (r). As the radius is halved, r becomes half of its original value. Plugging this new value of r into the gravitational potential equation, we get:
V' = -GM/(r/2) = -2GM/r
Comparing this with the original gravitational potential equation, we can see that the potential at the center has decreased by a factor of 2. Therefore, the correct answer is option 'B': Decreases.
Conclusion:
When a hollow spherical shell is compressed to half its radius, the gravitational potential at the center decreases. This is because the mass remains the same, but the distance from the center to any point within the shell is halved.
Attention Class 11 Students!
To make sure you are not studying endlessly, EduRev has designed Class 11 study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Class 11.
|
Explore Courses for Class 11 exam
|
|
Similar Class 11 Doubts
Top Courses for Class 11View all
A hollow spherical shell is compressed to half its radius. The gravitational potential at the centrea)Increasesb)Decreasesc)Remains samed)Ruring the compression increases then returns at the previous valueCorrect answer is option 'B'. Can you explain this answer?
Question Description
A hollow spherical shell is compressed to half its radius. The gravitational potential at the centrea)Increasesb)Decreasesc)Remains samed)Ruring the compression increases then returns at the previous valueCorrect answer is option 'B'. Can you explain this answer? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about A hollow spherical shell is compressed to half its radius. The gravitational potential at the centrea)Increasesb)Decreasesc)Remains samed)Ruring the compression increases then returns at the previous valueCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A hollow spherical shell is compressed to half its radius. The gravitational potential at the centrea)Increasesb)Decreasesc)Remains samed)Ruring the compression increases then returns at the previous valueCorrect answer is option 'B'. Can you explain this answer?.
A hollow spherical shell is compressed to half its radius. The gravitational potential at the centrea)Increasesb)Decreasesc)Remains samed)Ruring the compression increases then returns at the previous valueCorrect answer is option 'B'. Can you explain this answer? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about A hollow spherical shell is compressed to half its radius. The gravitational potential at the centrea)Increasesb)Decreasesc)Remains samed)Ruring the compression increases then returns at the previous valueCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A hollow spherical shell is compressed to half its radius. The gravitational potential at the centrea)Increasesb)Decreasesc)Remains samed)Ruring the compression increases then returns at the previous valueCorrect answer is option 'B'. Can you explain this answer?.
Solutions for A hollow spherical shell is compressed to half its radius. The gravitational potential at the centrea)Increasesb)Decreasesc)Remains samed)Ruring the compression increases then returns at the previous valueCorrect answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for Class 11.
Download more important topics, notes, lectures and mock test series for Class 11 Exam by signing up for free.
Here you can find the meaning of A hollow spherical shell is compressed to half its radius. The gravitational potential at the centrea)Increasesb)Decreasesc)Remains samed)Ruring the compression increases then returns at the previous valueCorrect answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
A hollow spherical shell is compressed to half its radius. The gravitational potential at the centrea)Increasesb)Decreasesc)Remains samed)Ruring the compression increases then returns at the previous valueCorrect answer is option 'B'. Can you explain this answer?, a detailed solution for A hollow spherical shell is compressed to half its radius. The gravitational potential at the centrea)Increasesb)Decreasesc)Remains samed)Ruring the compression increases then returns at the previous valueCorrect answer is option 'B'. Can you explain this answer? has been provided alongside types of A hollow spherical shell is compressed to half its radius. The gravitational potential at the centrea)Increasesb)Decreasesc)Remains samed)Ruring the compression increases then returns at the previous valueCorrect answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice A hollow spherical shell is compressed to half its radius. The gravitational potential at the centrea)Increasesb)Decreasesc)Remains samed)Ruring the compression increases then returns at the previous valueCorrect answer is option 'B'. Can you explain this answer? tests, examples and also practice Class 11 tests.
|
|
Explore Courses for Class 11 exam
|
|
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