The rotation of the earth having $R$ radius about its axis speeds up to a value such that a man at latitude angle $60^o$ feels weightlessness. The duration of the day in such a case is.
$2 \pi \sqrt{\frac{R}{g}}$
$ \pi \sqrt{\frac{R}{g}}$
$2 \pi \sqrt{\frac{g}{R}}$
$4 \pi \sqrt{\frac{R}{g}}$
The orbit of geostationary satellite is circular, the time period of satellite depends on $(i)$ mass of the satellite $(ii)$ mass of the earth $(iii)$ radius of the orbit $(iv)$ height of the satellite from the surface of the earth
A particle of mass $M$ is placed at the centre of a uniform spherical shell of mass $2M$ and radius $R$. The gravitational potential on the surface of the shell 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
The Earth is assumed to be a sphere of radius $R$. A platform is arranged at a height $R$ from the surface of the Earth. The escape velocity of a body from this platform is $fv$, where $v$ is its escape velocity from the surface of the Earth. the value of $f$ is
A geo-stationary satellite is orbiting the earth at a height of $5R$ above surface of the earth, $R$ being the radius of the earth. The time period of another satellite in hours at a height of $2R$ from the surface of earth is