Two stars of masses $m_1$ and $m_2$ are parts of a binary star system. The radii of their orbits are $r_1$ and $r_2$ respectively, measured from the centre of mass of the system. The magnitude of gravitational force $m_1$ exerts on $m_2$ is
$\frac{{{m_1}{m_2}G}}{{{{({r_1} + {r_2})}^2}}}$
$\frac{{{m_1}G}}{{{{({r_1} + {r_2})}^2}}}$
$\frac{{{m_2}G}}{{{{({r_1} + {r_2})}^2}}}$
$\frac{{G({m_1} + {m_2})}}{{{{({r_1} + {r_2})}^2}}}$
A geo-stationary satellite is orbiting the earth at a height of $6 R$ above the surface of earth, $R$ being the radius of earth. The time period of another satellite at a height of $2.5 R$ from the surface of earth is
Three identical bodies of equal mass $M$ each are moving along a circle of radius $R$ under the action of their mutual gravitational attraction. The speed of each body is
A rocket is projected in the vertically upwards direction with a velocity kve where $v_e$ is escape velocity and $k < 1$. The distance from the centre of earth upto which the rocket will reach, will be
The kinetic energy needed to project a body of mass $m$ from the earth's surface (radius $R$) to infinity is
If the gravitational acceleration at surface of Earth is $g$ , then increase in potential energy in lifting an object of mass $m$ to a height equal to half of radius of earth from surface will be