work due to gravity

Question

The force pulling an object to earth is  where G is the gravitational constant, M is the mass of the Earth, m is the mass of the object, and r is the distance between the object and the center of the Earth. Let R represent the radius of the Earth. How much work is required to move the object infinitely far from Earth?

a.  infinite
b. 0
c. (GMm)/R
d. G+MR²

Answer 1

F= GmM/r^2

To find work we integrate force over distance

 

Work = int (gmM/r^2) dr   from r= R to r=infinity

 

Antiderivative is -GmM/r.

Evaluate at limits to get GmM/R   (C)