Question

Let V and E be the gravitational potential and gravitational field at a distance r from the centre of a uniform spherical shell. Consider the following two statements
(A) The plot of V against r is discontinuous.
(B) The plot of E against r is discontinuous.
(a) Both A and B are correct.
(b) A is correct but B is wrong.
(c) B is correct but A is wrong.
(d) Both A and B are wrong.

Answer 1

(A) The plot of V against r is discontinuous.

(B) The plot of E against r is discontinuous.

On considering the above two statements, (d) both A and B are wrong

Explanation :

• The statement A is wrong because, at the center, V’s value is -3GM/2a and it continuously increases at infinity from -GM/a to zero at the surface to -GM/a at the surface continuously.
• Hence, this is continuous.
• The statement B is wrong because, E’s value linearly rises to zero in the center to GM/a² at the surface.
• Then, it surges to zero at the infinity from GM/a² at the surface. Hence, this is also continuous.
• So, both these statements are wrong.