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Question
A uniform spherical shell gradually shrinks maintaining its shape. The gravitational potential at the centre.
A uniform spherical shell gradually shrinks maintaining its shape. The gravitational potential at the centre.
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Solution
The correct option is B Increases
We know that for a spherical shell the potential is given as V=−GMR the negative sign shows that any mass will be attracted towards the shell, gravitational potential is always negative.
Now if the shell is shrinking maintaining its shape that is its still spherical so the above formula is still applicable. then as R decreases the term GM/R increases so the potential will increase.
Don't worry about the sign because it just shows that if we bring some body from infinity to a place where potential is negative we will get the work i.e. we don't have to do any work, work will be obtained by us.
Option A is correct.
We know that for a spherical shell the potential is given as V=−GMR the negative sign shows that any mass will be attracted towards the shell, gravitational potential is always negative.
Now if the shell is shrinking maintaining its shape that is its still spherical so the above formula is still applicable.
then as R decreases the term GM/R increases so the potential will increase.
Don't worry about the sign because it just shows that if we bring some body from infinity to a place where potential is negative we will get the work i.e. we don't have to do any work, work will be obtained by us.
Option A is correct.
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