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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?
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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
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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.
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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?
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