A satellite of mass m revolving in a circular orbit of radius $r$ around the earth has kinetic energ

Question

A 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\

Professor PC Thomas Classes · Answer

D)If $m$ is the mass and $v$ is the orbital velocity of the satellite, then its kinetic energy $$ \mathrm{E}=\frac{1}{2} \mathrm{~m} v^{2} $$ $$ m=\frac{1}{2} m^{2} v^{2} $$ (i) $$ \mathrm{m}^{2} v^{2}=2 \mathrm{Em} $$ If $r$ is the radius of the orbit of the satellite, then its angular momentum $$ \mathrm{L}=\mathrm{mvr} $$ Using Eq. (i), $$ \mathrm{L}=(\sqrt{2 \mathrm{Em}}) \mathrm{r}=\sqrt{2 \mathrm{Emr}^{2}} $$