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प्रश्न
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.
उत्तर
Given: gd = 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: gd = `"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%.
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