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Potential Energy of an Object at a Height

There is a sm...

Question

There is a small hole in a spherical shell of mass M and radius R. A particle of mass m is dropped from point A as shown. Match the two columns for the situation shown in figure.

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Solution

Since $U_{G} = - G M m / r$ outside the sphere therefore, from A to B continously decreases.
A->2
potential energy inside a hollow sphere remains constant therefore,
B->4
Since potential energy is constant therefore, KE will rermain constant and so as velocity of particle.
C->4
Since, gravitstional force outside the sphere is $F_{G} = G M m / r^{3}$ therefore, from A to B acceleration increases then remains constant i.e zero inside the sphere.
D->3

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