#### The change in the value of  g   at a height  h above the surface of the earth is the same as at a depth   d   below the surface of earth. When both  d  and  h  are much smaller than the radius of earth, then which of the following is correct ? Option 1) Option 2) Option 3) Option 4)

As we learnt in

At height,

$\dpi{100} g_{h}=g\left ( 1-\frac{2h}{R} \right )where\; h< < R$

$\dpi{100} or\; \; g-g_{h}=\frac{2hg}{R}\; \; or\; \; \Delta \; g_{h}=\frac{2hg}{R}..........(i)$

$\dpi{100} At\; depth,\; g_{d}=g\left ( 1-\frac{d}{R} \right )where\; d< < R$

$\dpi{100} or\; \; g-g_{d}=\frac{dg}{R}$

$\dpi{100} or\; \; \Delta \; g_{d}=\frac{dg}{R}..........(ii)$

$\dpi{100} From\; \; (i)\; and\; (ii),when\; \Delta g_{h}=\Delta g_{d}$

$\dpi{100} \frac{2hg}{R}=\frac{dg}{R}\; or\; \; d=2h$

Value of g when h < < R -

Value of g decreases.

height above surface of earth

- wherein

% decrease

change in value of 'g'

Option 1)

Correct

Option 2)

Incorrect

Option 3)

Incorrect

Option 4)

Incorrect