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}}$
$2 \pi \sqrt{\frac{g}{R}}$
$4 \pi \sqrt{\frac{R}{g}}$
Starting from the centre of the earth having radius $R,$ the variation of $g$ (acceleration due to gravity) is shown by
Given that mass of the earth is $M$ and its radius is $R$. A body is dropped from a height equal to the radius of the earth above the surface of the earth. When it reaches the ground its velocity will be
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
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
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