A particle is kept at rest at a distance $'R'$ from the surface of earth (of radius $R$). The minimum speed with which it should be projected so that it does not return is
$\sqrt {\frac{{GM}}{{4R}}} $
$\sqrt {\frac{{GM}}{{2R}}} $
$\sqrt {\frac{{GM}}{{R}}} $
$\sqrt {\frac{{2GM}}{{R}}} $
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
The radius of a planet is $R$. A satellite revolves around it in a circle of radius $r$ with angular velocity $\omega _0.$ The acceleration due to the gravity on planet’s surface is
Asatellite is launched into a circular orbit of radius $R$ around the earth. A second satellite is launched into an orbit of radius $1.02\,R.$ The period of second satellite is larger than the first one by approximately ........ $\%$
A satellite in force free space sweeps stationary interplanetary dust at a rate of $\frac{d M}{d t}=\alpha v$ where $M$ is mass and $v$ is the speed of satellite and $\alpha$ is a constant. The acceleration of satellite is
The angular speed of earth in $rad/s$, so that bodies on equator may appear weightless is : [Use $g = 10\, m/s^2$ and the radius of earth $= 6.4 \times 10^3\, km$]