Correct Answer - Option 2 :
300 km
The correct answer is option 2) i.e. 300 km
CONCEPT:
-
Acceleration due to gravity on the surface of Earth of mass M and radius Re is denoted by g.
- It has an approximated uniform value of 9.8 m/s2 on the surface of Earth.
The acceleration due to gravity at a depth 'd' below the surface of Earth is given by:
\(\Rightarrow g' = g(1- \frac{d}{R_e})\)
The acceleration due to gravity at a height 'h' above the surface of Earth is given by:
\(⇒ g'' = g(1+ \frac{h}{R_e})^{-2}\)
\(⇒ g'' = g(1- \frac{2h}{R_e})\) for h << Re
CALCULATION:
Given that:
At h = 150 km and the depth 'd', the acceleration due to gravity has the same value i.e. g' = g"
\( \Rightarrow g(1- \frac{D}{R_e}) = g(1- \frac{2h}{R_e}) \)
\(\Rightarrow (R_e-D) = (R_e - 2h) \)
\(\Rightarrow D = 2h = 2(150) = 300\: km\)
Thus, the distance 'D' from the surface of Earth is 300 km.
