5. The ratio of the acceleration due to gravity at the surface of the Earth to that at a height equal to the radius of the Earth is:
To find the value of \( g \) at a height equal to the Earth's radius (\( h = R \)), we use the formula:
\( g_h = g \left( \frac{R}{R + h} \right)^2 \)
Substituting \( h = R \):
\( g_h = g \left( \frac{R}{R + R} \right)^2 \)
Simplify:
\( g_h = g \left( \frac{R}{2R} \right)^2 \)
\( g_h = g \left( \frac{1}{2} \right)^2 \)
\( g_h = g \cdot \frac{1}{4} \)
\(g/ g_h = \frac{4}{1} \)
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