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 x is equal to.

• A. h
• B. 2h
• C. $\frac{h}{2}$
• D. 4h

Answer 1

The correct option is B 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 $x=2h$