Question

# Value of acceleration due to gravity is maximum at,A.) At center of earthB.) At surface of earthC.) At a height of 50 km from earth’s surfaceD.) At a height of 12 km from earth’s surface

Hint: The acceleration due to gravity varies as we go up or down the surface of earth. Consider what happens when we go very high from earth and reach a point in outer space. What happens to acceleration due to gravity at that time?

The acceleration due to gravity is the acceleration attained by a body in vacuum while it is free falling or falling under gravity alone. This acceleration is caused by the gravitational attraction of the planet and the body. The acceleration due to gravity depends on the mass of the planet where the object is dropped and the distance between the plane and the object. It is denoted by ‘g’. The acceleration due to gravity for a planet of mass M and radius R is given by,
$\text{g}=\dfrac{\text{GM}}{{{\text{R}}^{\text{2}}}}$
Where, G is the gravitational constant.
The above equation gives the acceleration due to gravity value at the surface of the earth. So what happens if you take the object up or down the surface of the earth?
The change in acceleration due to gravity at a height h above the surface of the earth is given by,
${{g}_{h}}=\dfrac{g}{{{\left( 1+\dfrac{h}{R} \right)}^{2}}}$
Where,
${{\text{g}}_{\text{h}}}$ is the acceleration due to gravity at a height ‘h’ from earth.
g is the acceleration due to gravity at the surface of the earth.
From the equation it is clear that as h increases the value of g decreases.

The value of g at a depth ‘d’ from the surface of the earth is given by the formula
${{g}_{d}}=g\left[ 1-\dfrac{d}{R} \right]$
Where,
${{\text{g}}_{\text{d}}}$ is the acceleration due to gravity at a depth ‘d’ from earth.
g is the acceleration due to gravity at the surface of the earth.
So the value of g decreases as we go to a depth from the surface of the earth. So the maximum value of g is at the surface of the earth.
So the answer to the question is option (B)- At the surface of earth.

Note: The value of acceleration due to gravity at the center of the earth is zero.
The object is said to be at infinity if acceleration due to gravity on the object above the surface of the earth is zero.