Question

The change in the value ${}^{\prime }{g}^{\prime }$ at a height ${}^{\prime }{h}^{\prime }$ above the surface of the earth is the same as at a depth ${}^{\prime }{d}^{\prime }$ below the surface of earth. When both ${}^{\prime }{d}^{\prime }$ and ${}^{\prime }{h}^{\prime }$ are much smaller than the radius of earth, then which one of the fol lowing is correct?

• A. $d=h$
• B. $d=2h$
• C. $d=\frac{2h}{2}$
• D. $d=\frac{h}{2}$

Answer 1

The correct option is B $d=2h$

Acceleration due to gravity at a depth 'd' from earth surface is:

$g_d=g(1-\frac{d}{R})$

Acceleration due to gravity at height 'h' from earth surface is: he is very much smaller than R.

$g_h=g(1-\frac{2h}{R})$

$g_h=g_d$

By solving it, $d=2h$.