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/s^{2} = 10^{3} m/s^{2}
\(⇒ g'' = g(1 \frac{2h}{R_e})\)
\(⇒ 10^{3}= 10(1 \frac{2h}{6400})\)
⇒ h = 3200 km
Therefore, distance from the centre of earth = R + h = 6400 + 3200 = 9600 km.