Q131 / 160 · TS EAMCET 2023 (13 May Shift 2) · Physics

The ratio of orbital velocity of a body near to the surface of a planet and escape velocity of a body from the surface of the same planet is

  • A
    $\sqrt{2}: 1$
  • B
    $\sqrt{5}: 1$
  • Correct answer
    C
    $1: \sqrt{2}$
  • D
    $1: \sqrt{5}$

Solution

$\begin{aligned} & \text {Orbital velocity }=\sqrt{\frac{\mathrm{GM}}{\mathrm{r}}} \\ & \text { Escape velocity }=\sqrt{\frac{2 \mathrm{GM}}{\mathrm{r}}} \\ & \text { Ratio }=\frac{\sqrt{\frac{\mathrm{GM}}{\mathrm{r}}}}{\sqrt{\frac{2 \mathrm{GM}}{\mathrm{r}}}}=\frac{1}{\sqrt{2}}\end{aligned}$

Hence, the correct answer is option: 'C'.

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