The orbital angular momentum of a satellite revolving at a distance $r$ from the centre is $L$. If the distance is increased to $4r$,then the new angular momentum will be

The height of a geostationary satellite is approximately ........ $km$.

Two satellites $A$ and $B$ of masses $200 \, kg$ and $400 \, kg$ are revolving around the Earth at heights of $600 \, km$ and $1600 \, km$ respectively. If $T_{A}$ and $T_{B}$ are the time periods of $A$ and $B$ respectively,then find the value of $T_{B} - T_{A}$.
[Given: Radius of Earth $R = 6400 \, km$,Mass of Earth $M = 6 \times 10^{24} \, kg$,$G = 6.67 \times 10^{-11} \, Nm^{2}/kg^{2}$]

An artificial satellite is revolving around a planet of radius $R$ in a circular orbit of radius $a$. If the time period of revolution of the satellite $T \propto a^{3/2} g^x R^y$,then the values of $x$ and $y$ are respectively. [Note: $g$ is the acceleration due to gravity at the surface of the planet.]

Consider a binary star system of star $A$ and star $B$ with masses $m_{A}$ and $m_{B}$ revolving in a circular orbit of radii $r_{A}$ and $r_{B}$,respectively. If $T_{A}$ and $T_{B}$ are the time periods of star $A$ and star $B$,respectively,then -

Shown are several curves [fig. $(a)$,$(b)$,$(c)$,$(d)$,$(e)$,$(f)$]. Explain with reason,which ones amongst them can be possible trajectories traced by a projectile (neglect air friction).