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प्रश्न
Answer the following question in detail.
State the formula for the acceleration due to gravity at depth ‘d’ and altitude ‘h’. Hence show that their ratio is equal to `(("R - d")/("R - 2h"))` by assuming that the altitude is very small as compared to the radius of the Earth.
उत्तर
- For an object at depth d, acceleration due to gravity of the Earth is given by,
`"g"_"d" = "g"(1 - "d"/"R")` ....(1) - Also, the acceleration due to gravity at smaller altitude h is given by,
`"g"_"h" = "g"(1 - "2h"/"R")` ....(2) - Hence, dividing equation (1) by equation (2), we get,
`"g"_"d"/"g"_"h" = ("g"(1 - "d"/"R"))/("g"(1 - "2h"/"R")) = ("R - d")/"R" xx "R"/("R - 2h")`
∴ `"g"_"d"/"g"_"h" = ("R - d")/("R - 2h")`
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