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Can two particles be in equilibrium unde...

Can two particles be in equilibrium under the action of their mutual gravitational force? Can three particle be? Can one of the three particles be?

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Two particles of equal mass go round a circle of radius R under the action of their mutual gravitational attraction. Find the speed of each particle.

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Knowledge Check

  • Two particles of equal mass go around a circle of radius R under the action of their mutual gravitational attraction. The speed v of earth particle is

    A
    `(1)/(3)sqrt((Gm)/(R ))`
    B
    `(1)/(2)sqrt((Gm)/(R ))`
    C
    `(1)/(2)sqrt((R )/(Gm))`
    D
    `sqrt((Gm)/(R ))`

  • Two identical particles of mass 1 kg each go round a circle of radius R, under the action of their mutual gravitational attraction. The angular speed of each particle is :

    A
    `sqrt((G)/(2R^(3)))`
    B
    `1/2sqrt((G)/(R^(3)))`
    C
    `1/(2R)sqrt(1/G)`
    D
    `sqrt((2G)/(R^(3)))`

  • Two particles of equal mass m go around a circle of radius R under the action the of their mutual gravitational attraction . The speed v of each particle is

    A
    `1/2 sqrt((Gm)/R)`
    B
    `sqrt((4GM)/R)`
    C
    `1/(2R) sqrt(1/(Gm))`
    D
    `sqrt((Gm)/(2R))`

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