What will be the acceleration due to gravity at the centre of earth?

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.
• The acceleration produced in the motion of a body under the effect of gravity is called acceleration due to gravity, it is denoted by g.
• If g is the acceleration due to gravity, then

• Now as we move below the surface the variation of gravitational acceleration g_d can be expressed as

Here,

R = the radius of the planet,

g = the acceleration due to gravity on the surface,

g_d = the acceleration due to gravity at some depth,

d = the depth from its surface.

Explanation:

As explained above the acceleration due to gravity at any depth is given as

Now if we dig and reach at the centre of the earth the depth will be given as, d = R

Hence at depth acceleration due to gravity will be zero.