A satellite is orbitting around the earth with areal speed $v_a$. At what height from the surface of the earth, it is rotating, if the radius of earth is $R$
$\frac{{4v_a^2}}{{g{R^2}}} - R$
$\frac{{2v_a^2}}{{g{R^2}}} - R$
$\frac{{v_a^2}}{{g{R^2}}} - R$
$\frac{{v_a^2}}{{2g{R^2}}} - R$
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
If the radius of the earth were shrink by $1\%$ and its mass remaining the same, the acceleration due to gravity on the earth's surface would
The escape velocity from a planet is $V_e.$ A tunnel is dug along the diameter of the planet and a small body dropped into it. The speed of the body at the centre of the planet will be
Imagine a light planet revolving around a very massive star in a circular orbit of radius $R$ with a period of revolution $T$. If the gravitational force of attraction between the planet and the star is proportional to $R^{-5/2}$, then,
A satellite can be in a geostationary orbit around a planet at a distance $r$ from the centre of the planet. If the angular velocity of the planet about its axis doubles, a satellite can now be in a geostationary orbit around the planet if its distance from the centre of the planet is