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Q.
The satellite of mass $m$ revolving in a circular orbit of radius $r$ around the earth has kinetic energy $E$ . Then its angular momentum will be
NTA AbhyasNTA Abhyas 2022
Solution:
If $m$ is the mass and $v$ is the orbital velocity of the satellite, then kinetic energy.
$ \, E=\frac{1}{2}m v^{2}$
$or \, \, Em=\frac{1}{2}m^{2}v^{2}$
$or \, m^{2}v^{2}=2Em$
$or \, \, \, mv=\sqrt{2 E m} \, \, \, \ldots .\left(i\right)$
$ \, $ If $r$ is the radius of the orbit of the satellite, then its angular momentum
$ \, L=mvr$
Using Eq. $\left(\right.i\left.\right)$ ,
$ \, \, \, L=\left(\sqrt{2 E m}\right)r=\sqrt{\left(2 E m r\right)^{2}}$