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 satellite $S$ is moving in an elliptical orbit around the earth. The mass of the satellite is very small compared to the mass of the earth. Then
The distance of neptune and saturn from the sun is nearly $10^{13}$ and $10^{12}$ meter respectively. Assuming that they move in circular orbits, their periodic times will be in the ratio
Time period of simple pendulum increases by an amount $\sqrt 2 $ times at height $'h'$ from the surface of earth. Then the value of $h$ is
Suppose the gravitational force varies inversely as the $n^{th}$ power of the distance. Then, the time period of a planet in circular orbit of radius $R$ around the sun will be proportional to
A spherical part of radius $R/2$ is excavated from the asteroid of mass $M$ as shown in the figure. The gravitational acceleration at a point on the surface of the asteroid just above the excavation is