Question

Two particles of masses m and 9m are separated by a distance r. At a point on the line joining them the gravitational field is zero. The gravitational potential at that point is ______.

( G = universal constant of gravitation)

Options

• `-(4"Gm")/"r"`

• `-(8"Gm")/"r"`

• `-(16"Gm")/"r"`

• `-(32"Gm")/"r"`

Answer 1

Two particles of masses m and 9m are separated by a distance r. At a point on the line joining them the gravitational field is zero. The gravitational potential at that point is `underlinebb(-(16"Gm")/"r")`.

( G = universal constant of gravitation)

Explanation:

Let P be the point where gravitational field is zero so,

`"Gm"/x^2=("G"9"m")/("r"-x)^2`

⇒ `1/x^2=9/("r"-x)^2`

⇒ `sqrt(("r"-x)^2) = sqrt(9x^2)`

⇒ r - x = 3x

⇒ x = `"r"/4`

Now, gravitational potential at this point is

`-((4"Gm")/"r"+("G"9"m"xx4)/(3"r"))[
"r"-x= (3"r")/4]`

⇒ `-((4"Gm"+12"Gm")/"r")`

⇒ `-(16"Gm")/"r"`