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

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

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

\({g_d} \propto \left( {R - d} \right) \Rightarrow {g_d} = g\left( {1 - \frac{d}{R}} \right)\)

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

\({g_d} = g\;\left( {1 - \frac{d}{R}} \right)\)

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

\(\therefore {g_d} = g\;\left( {1 - \frac{R}{R}} \right) = g \times 0 = 0\;m/{s^2}\)

Hence at depth acceleration due to gravity will be zero.