Question

At what distance below the surface of the Earth, the acceleration due to gravity decreases by 10% of its value at the surface, given the radius of Earth is 6400 km.

Answer 1

Given: g_d = 90% of g i.e., `"g"_"d"/"g"` = 0.9,
R = 6400 km = 6.4 × 10⁶ m

To find: Distance below the Earth’s surface (d)

Formula: g_d = `"g"(1 - "d"/"R")`

Calculation: From formula,

`"g"_"d"/"g" = (1 - "d"/"R")`

∴ `"d"/"R" = 1 - "g"_"d"/"g"`

∴ d = R`(1 - "g"_"d"/"g")`

= 6.4 × 10⁶ × 0.1

= 640 × 10³ m

= 640 km

At distance 640 km below the surface of the Earth, value of acceleration due to gravity decreases by 10%.