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
$\frac{{{m_1}{m_2}G}}{{{{\left( {{r_1} + {r_2}} \right)}^2}}}$
$\frac{{{m_1}G}}{{{{\left( {{r_1} + {r_2}} \right)}^2}}}$
$\frac{{{m_2}G}}{{{{\left( {{r_1} + {r_2}} \right)}^2}}}$
$\frac{{G({m_1} + {m_2})}}{{{{\left( {{r_1} + {r_2}} \right)}^2}}}$
Figure shows the variation of the gravitatioal acceleration $a_g$ of four planets with the radial distance $r$ from the centre of the planet for $r\geq $ radius of the planet. Plots $1$ and $2$ coincide for $r\geq R_2$ and plots $3$ and $4$ coincide for $r \geq R_4$. The sequence of the planets in the descending order of their densities is
The variation of acceleration due to gravity $g$ with distance $d$ from centre of the earth is best represented by ($R =$ Earth's radius)
Suppose, the acceleration due to gravity at the Earth's surface is $10\, m\, s^{-2}$ and at the surface of Mars it is $4.0\, m\, s^{-2}$. A $60\, kg$ pasenger goes from the Earth to the Mars in a spaceship moving with a constant velocity. Neglect all other objects in the sky. Which part of figure best represents the weight (net gravitational force) of the passenger as a function of time?
An object is taken to height $2 R$ above the surface of earth, the increase in potential energy is $[R$ is radius of earth]
A body of mass $m$ is situated at a distance equal to $2R$ ($R-$ radius of earth) from earth's surface. The minimum energy required to be given to the body so that it may escape out of earth's gravitational field will be