Facts for a uniform spherical shell

For a thin uniform spherical shell of mass $M$ and radius $R$:

• The gravitational field inside the shell is $\vec{g}=0$
• The gravitational potential at any interior point is constant and equal to the value at the surface: $V=-\frac{GM}{R}$

Check each statement

(1) The gravitational field is zero
This is true.

(2) The gravitational potential is zero
This is false. Inside the shell, $V=-\frac{GM}{R}\neq 0$ taking zero potential at infinity.

(3) The gravitational field is same everywhere
This is true inside the shell, because it is zero at every interior point.

(4) The gravitational potential is same everywhere
This is true inside the shell, because it is constant throughout the interior.

(5) All of the above
This is false, since statement (2) is false.

Select the correct option

True statements are: $(1), (3), (4)$

Hence the correct option is: $\boxed{\text{A}}$

Comparison with stored answer

Stored correct answer: $\text{A}$
Derived answer: $\text{A}$

So they agree.