Question

The acceleration due to gravity of Earth at a height above the surface of Earth is 1 mm/s². The distance of this location from the centre of Earth is (Assume g = 10 m/s², radius of earth = 6400 km)

1.

3200 km

2.

7650 km

3.

8640 km

4.

9600 km

Answer 1

Correct Answer - Option 4 :

9600 km

The correct answer is option 4) i.e. 9600 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 

​\(⇒ g' = g(1- \frac{d}{R_e})\)

• 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

EXPLANATION:

Given that:

g'' = 1 mm/s² = 10^-3 m/s²

\(⇒ g'' = g(1- \frac{2h}{R_e})\)

\(⇒ 10^{-3}= 10(1- \frac{2h}{6400})\)

⇒ h = 3200 km 

Therefore, distance from the centre of earth = R + h = 6400 + 3200 = 9600 km.