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Three uniform spheres each having a mass...

Three uniform spheres each having a mass M and radius a are kept in such a way that each touches the other two. Find the magnitude of the gravitational force on any of the spheres due to the other two.

Text Solution

Verified by Experts

The correct Answer is:
A, B, C, D
`F_("net") = sqrt(F^(2) + F^(2) + 2FF cos 60^(@))`

`= sqrt(3) F`
`= sqrt(3) (GMM)/((2a)^(2)) = (sqrt3 GM^(2))/(4a^(2))`
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Knowledge Check

  • Three uniform spheres each of mass m and diameter D are kept in such a way that each touches the other two, then magnitudes of the gravitational force on any one sphere due to the other two is

    A
    `(3Gm^(2))/(D^(2))`
    B
    `(2sqrt(3)Gm^(2))/(D^(2))`
    C
    `(sqrt(3Gm^(2)))/(4D^(2))`
    D
    `(sqrt(3)Gm^(2))/(D^(2))`

  • Three identical spheres, each having a charge q and radius R. are kept in such a way that each touches the other two. The magnitude of the electric force on any sphere due to the other two is

    A
    `(1)/(4 pi epsilon_(0))((q)/(R ))^(2)`
    B
    `(sqrt(3))/(4 pi epsilon_(0))((q)/(R ))^(2)`
    C
    `(sqrt(3))/(16 pi epsilon_(0))((q)/(R ))^(2)`
    D
    `(sqrt(5))/(16 pi epsilon_(0))((q)/(R ))^(2)`

  • Three uniform spheres, A, B and C each of mass M and radius R are kept in such a way that each sphere touches the other two. What is the magnitude of the gravitational force acting on A due to B and C ?

    A
    `(sqrt(3)GM^(2))/(4R^(2))`
    B
    `(sqrt(3)GM^(2))/(R^(2))`
    C
    `(3GM^(2))/(4R^(2))`
    D
    `(sqrt(3)GM^(2))/(2R)`