Question

If the value of ‘g’ at a height h above the surface of the earth is the same as at a depth x below it, then (both x and h being much smaller than the radius of the earth)

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

Answer 1

The correct option is B $x=2h$

The value of g at the height h from the surface of earth
$g^{{}^{\prime }}=g(1-\frac{2h}{R})$
The value of g at depth x below the surface of earth
$g^{{}^{\prime }}=g(1-\frac{x}{R})$
These two are given equal, hence $g^{{}^{\prime }}=g(1-\frac{2h}{R})=g^{{}^{\prime }}=g(1-\frac{x}{R})$
On solving, we get $x=2h$