A person moves from a point 16 km below the Earth's surface to a point 16 km above the Earth's surface. Find the approximate percentage change in acceleration due to gravity g.
Given:
For small depths and heights compared with Earth's radius:
At depth d:
gd = g(1 − d/R)
At height h:
gh = g(1 − 2h/R)
Given:
d = h = 16 km
R = 6400 km
The fractional change between these two values is:
Δg/g = (d/R)
= 16/6400
= 1/400
= 0.0025
Converting into percentage:
0.0025 × 100
= 0.25%
Because the depth and height are very small compared to Earth's radius, first-order approximations are sufficiently accurate. Such approximations are frequently used in competitive examinations to simplify calculations.
Therefore, the approximate percentage change in g is:
0.25%