TS EAMCET · Physics · Gravitation
Consider a spherical planet which is rotating about its axis such that the speed of a point on its equator is \(v\) and the effective acceleration due to gravity on the equator is \(\frac{1}{3}\) of its value at the poles. What is the escape velocity for a particle at the pole of this planet.
- A \(3 \mathrm{v}\)
- B \(2 \mathrm{v}\)
- C \(\sqrt{3} \mathrm{v}\)
- D \(\sqrt{2} v\)
Answer & Solution
Correct Answer
(C) \(\sqrt{3} \mathrm{v}\)
Step-by-step Solution
Detailed explanation
We know that the escape velocity of a particle from the surface of a planet is given by \[ \begin{aligned} v_e & =\sqrt{\frac{2 G M}{R}}=\sqrt{\frac{2 g R^2}{R}} \quad\left[\because G M=g R^2\right] \\ & =\sqrt{2 g R} \end{aligned} \] where, \(g=\) acceleration due to gravity,…
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