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Two bodies of masses m and 4m are placed...

Two bodies of masses m and 4m are placed at a distance r. The gravitational potential at a point on the line joining them where the gravitational field is zero is:

A

`-(4Gm)/(r)`

B

`-(8Gm)/(r)`

C

`-(16Gm)/(r)`

D

`-(32Gm)/(r)`

Text Solution

Verified by Experts

The correct Answer is:
C
`(M)/(m)=((x)/(2-x))^(2)`
`9=((x)/(r-x))^(2)`
`3=(x)/(r-x)`
`3r-3x=x`
`3r=4x`
`x=(3)/(4)r`
`:.y=(1)/(4)r`
`v=-(GM)/(x)-(Gm)/(y)`
`=-G[(9m)/((3)/(4)x)+(m)/((1)/(4)r)]`
`=-(Gm)/(r)[12+4]`
`=(16Gm)/(r)`
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Knowledge Check

  • Two bodies of mass m and 4m are placed at a distance r. The gravitational potential at a point on the line joining them where the gravitational field is zero is

    A
    zero
    B
    `(-4Gm)/(r )`
    C
    `(-6Gm)/(r )`
    D
    `(-9Gm)/(r )`

  • Two bodies of masses m and 4 m are placed at a distance r. The gravitational potential at a point on the line joining them where the gravitational field is zero, is

    A
    `-(4GM)/(r )`
    B
    `-(6 Gm)/(r )`
    C
    `-(9 Gm)/(r )`
    D
    zero

  • Two bodies of masses m and M are placed at distance d apart. The gravitational potential (V) at the position where the gravitational field due to them is zero V is

    A
    `V=-(G)/(d)(m+M)`
    B
    `V=-(G)/(d)`
    C
    `V=-(GM)/(d)`
    D
    `V=-(G)/(d)sqrt(sqrt(m)+sqrt(M))^(2)`

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