# 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 - Physics

Sum

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.

#### Solution

1. For an object at depth d, acceleration due to gravity of the Earth is given by,
"g"_"d" = "g"(1 - "d"/"R")      ....(1)
2. Also, the acceleration due to gravity at smaller altitude h is given by,
"g"_"h" = "g"(1 - "2h"/"R")      ....(2)
3. 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")
Concept: Variation in the Acceleration Due to Gravity with Altitude, Depth, Latitude and Shape
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#### APPEARS IN

Balbharati Physics 11th Standard Maharashtra State Board
Chapter 5 Gravitation
Exercises | Q 3. (xiv) | Page 98