Question

The value of gravitational intensity of the centre of earth is
A. 1
B. infinity
C. zero
D. none of these

Answer 1

Hint: The gravitational intensity is defined as the gravitational force per unit mass of an object which is equivalent to acceleration due to gravity. By putting the value of height equal to zero in the expression for the variation of acceleration of gravity with distance from the surface of earth, we can obtain the required answer.

Complete step by step answer:
The gravitational intensity of the earth can be defined as the gravitational force exerted by earth per unit mass of the object. Dimensionally, the force per unit mass is equal to the acceleration so we can say that we are talking about the acceleration due to gravity when we refer to the gravitational intensity of earth.
The variation of acceleration due to gravity with distance from the surface of earth is given as:
$g' = g\left( {1 - \dfrac{h}{R}} \right)$
Here g is the value of acceleration due to gravity on the surface of earth while g’ is the acceleration due to gravity at a distance h from the surface of earth. R represents the radius of earth.
Now at the centre of earth, the distance from the surface of earth is equal to the radius of earth. Using this information in the above equation, we get the value of acceleration due to gravity at the centre of earth to be
$g' = g\left( {1 - \dfrac{R}{R}} \right) = 0$
This means that the gravitational intensity or the acceleration due to gravity is equal to zero at the centre of earth.

So, the correct answer is “Option C”.

Note: The value of acceleration due to gravity is equal to $9.8m/{s^2}$ only near the surface of earth or at small distances from the surface of earth. With increase in distance from the surface of earth, the value of acceleration due to gravity goes on decreasing.