Gravitational problem - 11th Feb'16

Question

At what height from the earth does the acceleration due to gravity falls to !!1%!! that of the surface

a) !!9R!!
b) !!10R!!
d) !!100R!!
c) !!99R!!

Solution

Acceleration due to gravity on the earth surface, !!g = (GM)/R^2...(1)!!

Acceleration due to gravity a height h above the Earth's surface
!!g^' = (GM)/(R+h)^2....(2)!!

Given that !!g^' = 0.01 g!!

From equation (1) and (2), we will get

!!(GM)/(R+h)^2= (0.01)(GM)/R^2!!

!!=> 1/(R+h)^2 = 0.01/R^2!!

Taking squareroot both the sides,

!!=> 1/(R+h)= 0.1/R!!

!!=> 10R = R+h!!

!!=> h = 9R!!

Therefore, option (a) is correct.