Variation of Acceleration due to Gravity with Height and Depth – Rankers Physics

Acceleration Due to Gravity and its variation: Practice Problem & Solution

Consider earth to be a homogeneous sphere. Scientist A goes deep down in a mine and scientist B goes high up in a balloon. The value of g measured by:
A goes on decreasing and that by B goes on increasing
B goes on decreasing and that by A goes on increasing
Each decreases at the same rate
Each decrease at different rates

Solution Explained:

To solve this problem, we apply the core principles of Acceleration Due to Gravity and its variation. Understanding the underlying formula is key to arriving at the correct answer below:

Acceleration due to gravity decreases with depth as \( g_d = g(1 - \frac{d}{R}) \) and with height as \( g_h = g(1 - \frac{2h}{R}) \). Since the formulas and rates of decrease are different, they decrease at different rates.

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