Draw graphs showing the variation of acc...

Draw graphs showing the variation of accleeration due to gravity with (a) height above the Earth's surface, (b) depth below the Earth's surface.

Text Solution

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(a) The veriation of `g` with height `h` is related by ralation `g prop 1//r^(2)` where `r = R + h`. Thus, the variation of `g` and `r` is a parabolic curve, i.e., part `AB` of the graph, Fig.
(b) The variation of `g` with depth is related by equation `g' = g (1 - dl//R)` i.e., `g' prop (R - d)`. Thus, the variation of `g` and `d` is at st. line, i.e., part `AC` of the graph, Fig.

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The acceleration due to gravity at a height 1 km above the earth is the same as at a depth d below the surface of earth

d = 1 km

`d = (3)/(2) km`

d = 2 km

`d = (1)/(2)` km

The acceleration due to gravity at a height 1km above the earth is the same as at a depth d below the surface of earth. Then :

`d=1km`

`d=3/2km`

`d=2km`

`d=1/2km`

Let the acceleration due to gravity be g_(1) at a height h above the earth's surface g_(2) at a depth d below the earth's surface. If g_(1)=g_(2),h lt lt R and d lt lt R then

`h=d`

`h=2d`

`2h=d`

it is not possible for `g_(1)` to be equal to `g_(2)`