Question

Calculate 4th e depth below the surface of the earth where acceleration due to gravity becomes half of its value at the surface of the earth. Radius of the earth 6400km

Answer 1

Given

Radius of Earth (R) = 6400 km = 6400×10^{3}

Acceleration due to gravity (g) = 9.8 m/s^2

On certain depth acceleration due to gravity (g') = (9.8 m/s^2)/2 = 4.9 m/s^2

Now,

On depth (h) the acceleration due to gravity has the equation

g' = $\frac{g}{R}$ × (R-h)

4.9 = $\frac{9.8}{6400000}$ (6400000-h)

Solving this we get

h= 3200$10^{3}$ m

or, h=3200 km