First slide

Variation of g

Question

At a certain height above the earth’s surface, the gravitational acceleration is 4% of its value at the surface of the earth. Find the height. (R is the surface of the earth)

Easy

A

2R
B

4R
C

R
D

R/2

Solution

$\large \frac{{{g_h}}}{g} = \frac{{{R^2}}}{{{{(R + h)}^2}}}\therefore \frac{{R + h}}{R} = \sqrt {\frac{g}{{gh}}}$
$\large 1 + \frac{h}{R} = \sqrt {\frac{{g\left( {100} \right)}}{{4g}}} ;\frac{h}{R} = 4 \Rightarrow h = 4R$

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