The acceleration due to gravity at the centre of earth is

Concept:

Acceleration due to Gravity:

• The force of attraction exerted by the earth on a body is called gravitational pull or gravity.
• We know that when a force acts on a body, it produces acceleration. Therefore, a body under the effect of gravitational pull must accelerate.
• Variation in g with depth is given by:

\(⇒ g' = g\left[ {1 - \frac{d}{R}} \right]\)

Where is the g’ = Acceleration due to gravity at depth d, R = Radius of the earth, and g = Acceleration due to gravity at the surface of the earth

Explanation:

• At the center of the earth r = R, on putting in the equation we get 

• Hence the acceleration due to gravity at the center of the earth will be zero.  

Additional Information

The value of acceleration due to gravity is given as \(\Rightarrow g = \frac{{GM}}{{{R^2}}}\)

G is the universal gravitational constant, M is the mass of Earth, R is the radius of the earth. 

At some height h, the acceleration due to the gravity is given as

\(\Rightarrow g = \frac{{GM}}{{{(R+h)^2}}}\)