A satellite of mass 'm', revolving round the earth of radius 'r' has kinetic energy (E). Its angular…

A satellite of mass 'm', revolving round the earth of radius 'r' has kinetic energy (E). Its angular momentum is
  1. $\left(\mathrm{mEr}^{2}\right)^{\frac{1}{2}}$
  2. $\left(\mathrm{mEr}^{2}\right)$
  3. $\left(2 \mathrm{~m} \mathrm{Er}^{2}\right)^{\frac{1}{2}}$
  4. $\left(2 \mathrm{mEr}^{2}\right)$

Solution

$\begin{aligned} \mathrm{E}=\frac{1}{2} \mathrm{mV}^{2} \quad \therefore \mathrm{V} &=\sqrt{\frac{2 \mathrm{E}}{\mathrm{m}}} \\ \text { Angular momentum } \quad \mathrm{L} &=\mathrm{mvr} \quad=\mathrm{m} \cdot \sqrt{\frac{2 \mathrm{E}}{\mathrm{m}} \cdot \mathrm{r}} \\ &=\sqrt{2 \mathrm{mEr}^{2}}=\left(2 \mathrm{mEr}^{2}\right)^{\frac{1}{2}} \end{aligned}$

Asked in: MHT CET 2020 (14 Oct Shift 1)

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