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Two spheres each of mass M and radius R ...

Two spheres each of mass `M` and radius `R` are separated by a distance of `r`. The gravitational potential at the midpoint of the line joining the centres of the spheres is

A

`-(GM)/(r )`

B

`-(2GM)/( r)`

C

`-(GM)/(2 r)`

D

`-(4GM)/( r)`

Text Solution

Verified by Experts

The correct Answer is:
D
(d)
Let P is the midpoint of the line joining the centres of the spheres.
The gravitational potential at point P is
`V_(P)= -(GM)/(r//2)-(GM)/(r//2)=- (2GM)/(r )-(2GM)/( r)= -(4GM)/( r )`
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Knowledge Check

  • Two spheres each of mass M and radius R are separated by a distance of r . The gravitational potential at the potential at the midpoint of the line joining the centres of the spheres is

    A
    `-(GM)/r`
    B
    `-(2Gm)/r`
    C
    `-(GM)/(2r)`
    D
    `-(4GM)/r`

  • Two identical spheres each of mass M and Radius R are separated by a distance 10R. The gravitational force on mass m placed at the midpoint of the line joining the centres of the spheres is

    A
    zero
    B
    `(2GMm)/(25R^(2))`
    C
    `(GMm)/(25R^(2)`
    D
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  • Two heavy spheres of mass m are kept separated by a distance 2r. The gravitational field and potential at the midpoint of the line joining the centres of the spheres are

    A
    `(Gm^2)/(r^2)" and "0`
    B
    0 and `-(2Gm)/r`
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    D
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