Question

At what height from the earth's surface the acceleration due to gravity will be quarter of its value at the surface of earth? (Re = 6400 km)
Options
O 6400 km
4600 km
5000 km
2000 km
​

Answer 1

Answer:

Let the force of gravitational on an object of mass m at an altitude h from earth's surface be equal to F.

Radius of earth =Re=6400km

and mass of earth be Me.

F=G(Re+h)2Mem=mg′ 

So, g′=(Re+h)2GMe

g=Re2GMe

gg′=(Re+hRe)2=10064

Re+hRe=0.8

So the altitude =h=4Re