Inside a uniform spherical shell:
(a) The gravitational field is zero.
(b) The gravitational potential is zero.
(c) The gravitational field is the same everywhere.
(d) The gravitation potential is the same everywhere.
(e) All the above.
Choose the most appropriate answer from the options given below:

We recall the shell theorem, which states two key results for a thin, uniform, spherical shell of total mass $$M$$ and radius $$R$$:

1. For any internal point whose distance from the centre is $$r<R$$, the gravitational field (intensity) is zero:

$$\vec g(r)=0.$$

2. The gravitational potential at an internal point equals the potential at the surface and is therefore a constant given by

$$V(r)=V(R)=-\dfrac{GM}{R},$$

where $$G$$ is the universal gravitational constant. The minus sign shows the usual convention that potential is taken to be zero at infinity.

Now we examine each statement in the question:

    (a) “The gravitational field is zero.”  We have just established $$\vec g(r)=0,$$ so statement (a) is true.

    (b) “The gravitational potential is zero.”  From $$V(r)=-\dfrac{GM}{R},$$ the value is generally a non-zero negative constant (unless the mass itself is zero). Hence statement (b) is false.

    (c) “The gravitational field is the same everywhere.”  Because the field is identically zero at every internal point, every location experiences the same value (namely zero). So statement (c) is true.

    (d) “The gravitational potential is the same everywhere.”  We have $$V(r)=$$ constant for all internal points, so statement (d) is true.

    (e) “All the above.”  Since statement (b) is false, “all” cannot be correct, so (e) is false.

Combining the valid statements, only (a), (c) and (d) are correct. These correspond to Option A.

Hence, the correct answer is Option A.