Question

At the center of the earth, the value of g becomes:
A. Zero
B. Unity
C. Infinity
D. None of these

Answer 1

Hint To find the value we should keep in mind that the center of the earth will be a null point in all the force vectors. All the force acting by the two hemispheres will be nullifying at the center,i.e the force is countered from the parallel hemisphere.

Complete step-by-step solution :As we know that the acceleration due to gravity is varied in direct proportion to the subsequent distance from the center for a given point i.e $r$.
But when the value of $r > R$ the variation is directly proportional to $1/{r^2}$
So the expression for $g$will be given by $GM/{r^2}$
Subsequently when $r < R$, the value of $g = GMr/{R^3}$
So when the value of $r = 0$then the value of $g = 0$
The correct answer is i. Zero

Note: While calculating the value the comparison of r and R is necessary. Along with that the subsequent formulas should be implemented for the correct answers and any mismatch will lead to wrong answers. Apart from that the formulas for each case should ideally be remembered.