Question

at what depth below the surface of the earth is the value of g same as that at a height of 5 km​

Answer 1

At height h above the surface of earth ( for h<< R) g' = g(1–2h/R)

And at depth d below the surface of earth, g'= g(1-d/R)

As per question, g (1–2h/R) = g(1-d/R)

=> 2h = d => d = 2×5= 10 km

Answer 2

To find:

• Depth at which the value of 'g' is equal to that at a height of 5 km?

Calculation:

• Let the depth be d and the value of gravity be g''.

Also, for height h <<< R (radius of earth), we can say:

$g' = g \bigg(1 - \dfrac{2h}{R} \bigg)$

Now, this value of g' should be equal to g" at depth d :

$g' = g ''$

$\implies g \bigg(1 - \dfrac{2h}{R} \bigg) = g \bigg(1 - \dfrac{d}{R} \bigg)$

$\implies 1 - \dfrac{2h}{R} = 1 - \dfrac{d}{R}$

$\implies d = 2h$

$\implies d = 2 \times 5$

$\implies d = 10 \: km$

So, the value of depth 'd' is 10 km.