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 $R$
$\frac{{4v_a^2}}{{g{R^2}}} - R$
$\frac{{2v_a^2}}{{g{R^2}}} - R$
$\frac{{v_a^2}}{{g{R^2}}} - R$
$\frac{{v_a^2}}{{2g{R^2}}} - R$
A projectile is projected with velocity $k{v_e}$ in vertically upward direction from the ground into the space. (${v_e}$ is escape velocity and $k < 1)$. If air resistance is considered to be negligible then the maximum height from the centre of earth to which it can go, will be : (R = radius of earth)
A satellite moving with velocity $v$ in a force free space collects stationary interplanetary dust at a rate of $\frac{{dM}}{{dt}} = \alpha v$ where $M$ is the mass (of satellite + dust) at that instant . The instantaneous acceleration of the satellite is
At what height above the earth's surface is the value of $'g'$ is same as in a $200\, km$ deep mine ........ $km$
Two spheres of masses $m$ and $M$ are situated in air and the gravitational force between them is $F$. The space around the masses is now filled with a liquid of specific gravity $3$. The gravitationalforce will now be
At what altitude will the acceleration due to gravity be $25\% $ of that at the earth’s surface (given radius of earth is $R$) ?