Question

The ratio of the acceleration due to gravity as the bottom of a deep mine and that on the surface of the earth is 978/980. Find the depth of the mine, if the density of the earth is uniform throughout and the radius of the earth is 6300 km.

• A. 12.88 km
• B. 13.0 km
• C. 25.38 km
• D. 90.9 km

Answer 1

The correct option is A 12.88 km

Ratio of acceleration due to gravity
$\frac{g^{\prime }}{g}=\frac{978}{9800}=I-\frac{d}{R}$
$\frac{d}{R}=I-\frac{978}{9800}$
$d=\frac{2}{980}R$
$=\frac{2\times 6300}{980}$
= 12.86 km