Solve the integral `I=int_oo^R(GMm)/(x^2)dx`.

Options

A. `(-2GMm)/(R^2)`
B. `(-GMm)/(R^2)`
C. `(-GMm)/(R)`
D. `(+GMm)/(R)`

Answer

C

Explanation

`I=int_oo^R(GMm)/(x^2)dx=GMm int_oo^R(dx)/(x^2)=GMm[-1/x]_oo^R`
`=GMm[-1/R+1/oo]=(-GMm)/(R)`
The above expression represents gravitational potential energy which is obtained by integrating `GMm//x^2` between the limits infinity `(oo)` and radius of the earth (R).