Show that, for small distances compared with Earth’s radius , the altitude that…

PHYSICS · Subjective · CBSE · Physics · Gravitation · Gravitation

Problem

Show that, for small distances compared with Earth’s radius

R

, the altitude

h

that produces the same fractional decrease in

g

as a given depth

d

satisfies

h = d/2

. Hence calculate

h

when

d = 24\,\text{km}

and

R = 6.4 \times 10^{6}\,\text{m}