Question

What is the intensity of the gravitational field at the center of a spherical shell?

• A. Gm/r²
• B. g
• C. zero
• D. none of these

Answer 1

The correct option is C

zero

Explanation of the correct answer:

Option C

1. The intensity of the gravitational force at the center of the earth is zero.
2. The equation of the intensity of the gravitational force can be written as:
   $g\text{'}=g\left(1-\frac{H}{R}\right)$
   where $g$ is the acceleration due to gravity, $g\text{'}$ is the acceleration due to gravity at the distance $H$, $R$ is the radius of the earth.
3. At the center of the earth, the distance from the center of the earth from the surface is equal to its radius.
   The equation can be written as:
   $g\text{'}=g\left(1-\frac{R}{R}\right)=0$,
   Hence, the intensity of the gravitational field at the center of a spherical shell is zero.

Explanation of the incorrect Answers:

Option A

Gm/r²

1. The equation Gm/r² represented the gravity at the surface of the earth.
2. Gravity at the surface of the earth $9.8m{s}^{-2}$
3. The intensity of the gravitational field at the center of a spherical shell is zero.

Option B

g

1. the intensity of the gravitational field at the center of a spherical shell is zero.
2. The gravity is represented by the symbol g, but there is no gravity at the center of the spherical shell.

Hence, option C is the correct option.