A rocket is fired from the earth to the moon. The distance between the earth and the moon is r and the mass of the earth is 81 times the mass of the moon. The gravitational force on the rocket will be zero when its distance from the moon is

Options

A. `(r)/(20)`
B. `(r)/(15)`
C. `(r)/(10)`
D. `(r)/(5)`

Answer

c

Explanation

Let the rocket be at a distance x from the moon the gravitational force on it is zero. Its distance from earth `=r-x`. Gravitational force on rocket due to earth is
`F_(e)=(GmM_(e))/((r-x)^(2))`
Gravitational force on rocket due to moon is
`F_(m)=(GmM_(m))/(x^(2))`
`F_(e)=F_(m)`
`(r-x)/(x)=sqrt((M_(e))/(M_(m)))=sqrt(81)=9`
`x=(r)/(10)`