Discuss the variation of g with altitude.

Effect of Altitude on g:
Consider the Earth as a sphere with mass M, radius R , and center O . The acceleration due to gravity at a point on the surface of the Earth depends on its mass and radius. At a height h above the Earth’s surface, the gravity decreases due to the increased distance from the Earth’s center.

The gravity at the Earth’s surface is proportional to (1/R²), while at a height h, it is proportional to (1/(R + h)²). By comparing the two, the ratio of gravity at the height h to gravity at the surface can be expressed as ( (R/(R + h))²).

Using the binomial theorem for approximation when h is much smaller than R, the expression simplifies to show that the change in gravity is proportional to (1 – 2h/R). This means that as h increases, gravity decreases.

For very small heights compared to the Earth’s radius, higher-order terms in h/R can be ignored. This gives an approximate linear relationship showing a decrease in gravity with height.

Key Points:
– Gravity decreases with altitude because the distance from the Earth’s center increases.
– At greater heights, such as on mountains, the value of g is less than at lower elevations or plains.
– For significant heights relative to the Earth’s radius, the more accurate proportional relationship ((R/(R + h))²) should be used. For small heights, the approximate relationship (1 – 2h/R) suffices for practical calculations.