The change in the value of $g$ at a height ' $h$ ' above the surface of the earth is the same as at a depth…

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 one of the following is correct?
  1. $d=\frac{h}{2}$
  2. $\mathrm{d}=\frac{3 \mathrm{~h}}{2}$
  3. $\mathrm{d}=2 \mathrm{~h}$
  4. $\mathrm{d}= \mathrm{~h}$

Solution

$\frac{G M}{(R+h)^2}=\frac{G M}{R^3}(R-d)$ $\Rightarrow d=2 h$

Asked in: JEE Main 2005

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