Discuss variation of g with (A) Altitude(B) Depth

(A) Variation of g with Altitude:
The acceleration due to gravity, denoted by g, is not constant at different altitudes. It decreases as we move farther away from the Earth's surface. This variation occurs due to two main factors: the inverse square law and the distribution of mass in the Earth.

The inverse square law states that the gravitational force between two objects is inversely proportional to the square of the distance between their centers. As we move away from the Earth's surface, the distance between an object and the center of the Earth increases, leading to a decrease in the gravitational force acting on the object. Consequently, the acceleration due to gravity decreases with increasing altitude.

The distribution of mass in the Earth also affects the variation of g with altitude. The Earth is not a perfectly uniform sphere, and its mass is concentrated towards the center. As we move higher above the surface, we experience a smaller portion of the Earth's mass pulling us downwards. The mass above us exerts a weaker gravitational force compared to the mass beneath us, causing a reduction in the value of g.

In summary, as altitude increases, the acceleration due to gravity decreases. This decrease is primarily due to the inverse square law and the non-uniform distribution of the Earth's mass.

(B) Variation of g with Depth:
Unlike the variation with altitude, the variation of g with depth is not significant for most practical purposes. When we move deeper into the Earth's interior, the gravitational force acting on an object decreases slightly. However, this decrease is generally negligible compared to the effect of altitude on g.

The reason for the small variation of g with depth is that the Earth's mass is distributed over a much larger radius compared to the distances we typically encounter. As we descend into the Earth, the additional mass above us exerts a gravitational force in the opposite direction, partially canceling out the gravitational force from the mass beneath us. Therefore, the net effect on g due to depth is minimal.

It's worth noting that the Earth's core has a higher density than the surrounding mantle, and this difference in density does contribute to a slight increase in gravitational acceleration as we move towards the core. However, this effect is still relatively small and only becomes significant when considering extreme depths, such as those encountered in geophysical studies or deep mining.

In general, for most everyday situations and practical calculations, the variation of g with depth can be neglected, and it is sufficient to consider g as a constant value for a given location on the Earth's surface.