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

  • A

    $v = \frac{1}{{2R}}\,\sqrt {\frac{1}{{Gm}}} $

  • B

    $v = \sqrt {\frac{{Gm}}{{2R}}} $

  • C

    $v = \frac{1}{2}\,\sqrt {\frac{{Gm}}{R}} $

  • D

    $v = \sqrt {\frac{{4Gm}}{{R}}} $

Similar Questions

If the distance between the centres of Earth and Moon is $D$ and mass of Earth is $81\, times$ that of Moon. At what distance from the centre of Earth gravitational field will be zero?

A spherical planet far out in space has a mass ${M_0}$ and diameter ${D_0}$. A particle of mass m falling freely near the surface of this planet will experience an acceleration due to gravity which is equal to

If the change in the value of ' $g$ ' at a height ' $h$ ' above the surface of the earth is same as at a depth $x$ below it, then ( $x$ and $h$ being much smaller than the radius of the earth)

Two spheres of masses $m$ and $M$ are situated in air and the gravitational force between them is $F.$ The space around the masses is now filled with a liquid of specific gravity $3.$ The gravitational force will now be

A projectile is projected with velocity $k{v_e}$ in vertically upward direction from the ground into the space. (${v_e}$ is escape velocity and $k < 1)$. If air resistance is considered to be negligible then the maximum height from the centre of earth to which it can go, will be : (R = radius of earth)