Two bodies of masses .m. and .9m. are placed at a distance .r.. The gravitational potential at a point on the line joining them, where gravitational field is zero, is (G is universal gravitational constant )

Options

A. `(-14Gm)/( r)`
B. `(-16 Gm)/( r)`
C. `(-12Gm)/( r)`
D. `(-8Gm)/( r)`

Answer

B

Explanation

`m_1 =m`
`m_2=9m`
`d=r `
`x=(d)/(sqrt((m_2)/(m_1))+1)`
`x=( r)/(sqrt((9m)/(m))+1)`
`x=( r)/(4)`
`( r-x)=(r - r)/(4) =(3r)/(4)`.
Potential `v=v_(1)+v_(2)`
`=-(GM_1)/(x)-(GM_2)/((r-x))`
`=-(Gm)/(( r)/(4))-(G(9m))/((3r)/(4))`
`=-(4Gm)/( r) -(12 Gm)/( r) rArr =(-16Gm)/( r)` .