Question

At what depth the acceleration due to gravity is 9.45 m/s2 ? The acceleration due to gravity near the earth's surface is 9.8 m/s2, and the earth's radius is 6,400 km.

Answer 1

$g = \frac{gc \times m}{ {r}^{2} } \\ 9.45 = \frac{6.674 \times {10}^{ - 11} \times 5.972 \times {10}^{24} }{ {r}^{2} } \\ r = \sqrt{ \frac{(6.674 \times 5.972) \times {(10)}^{ - 11 + 24} }{9.45} } \\ r = \sqrt{ \frac{39.857 \times {10}^{13} }{9.45} } \\ r = \sqrt{4.217 \times {10}^{13} } \\ r = 6493.843km \\ \\ depth = 6400 - 6493.843 \\ = - 93.843km$
NOTE : gc = gravitational constant

Please Note ::: -93.843km means "93.843km" above the earth's surface...