Question

the distance below the surface of the earth where acceleration due to gravity becomes 90% of its value at the surface of earth is(radius of earth =6400km)
(1)160km
(2)320km
(3)640km
(4)480km​

Answer 1

Answer:

1775.774

Explanation:

gravity =gravitation constant ×mass of planet /redius of planet = 9.8

90 percent of 9.8

$9.8 \times \frac{90}{100} = 8.82$

9.8 + 8.82= 19.62

that is

$18.62 = 6.67 \times {10}^{ - 11} \times \frac{5.972 \times 10 {}^{24} }{distance {}^{2} }$

mass of Earth is 5.972 ×10^24kg

$distance {}^{2} \: = 6.67 \times 10 {}^{ - 11} \times \frac{5.972 \times 10 {}^{24} }{18.62}$

distance =4625.226 km (roughly)

depth =6400-4624.226 = 1775.774