Question

At a certain height above the Earth's surface the gravitational acceleration is 4% of its value at the surface of the earth. Find the height (R is the surface of the earth)

Answer 1

Let the acceleration due to gravity at the earth surface be g.

Then, the value of g at the height h= 4%of g= 4g/100= g/25

We know that acceleration due to gravity at a height h from the surface of the earth = g(R/R+h)², where R is the radius of the earth and g is the acceleration due to gravity at earth's surface and h is the height from earth's surface.

So, g/25= g(R/R+h)²

=>1/25=(R/R+h)² [g will cancel out]

=>1/5= R/R+h [ Doing square root both sides]

=>R+h=5R [ cross multiplication]

=>h = 4R

The body is at a height of four times the radius of earth from the surface of earth.