Question:
The ratio of the escape velocity to the orbital velocity of the earth is ________.
The ratio of the escape velocity to the orbital velocity of the earth is ________.
Show Hint
Escape velocity is always $\sqrt{2}$ times the orbital velocity for the same planet.
Updated On: Jun 26, 2026
- 2
- $\sqrt{2}$
- $\frac{1}{\sqrt{2}}$
- $\frac{1}{2}$
- $\sqrt{3}$
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Verified By Collegedunia
The Correct Option is B
Solution and Explanation
Step 1: Concept
Escape velocity $v_e = \sqrt{\frac{2GM}{R}}$ and Orbital velocity $v_o = \sqrt{\frac{GM}{R}}$.
Step 2: Meaning
We need the ratio $\frac{v_e}{v_o}$.
Step 3: Analysis
$\frac{v_e}{v_o} = \frac{\sqrt{2GM/R}}{\sqrt{GM/R}} = \sqrt{2}$.
Step 4: Conclusion
The ratio is $\sqrt{2} : 1$. Final Answer: (B)
Escape velocity $v_e = \sqrt{\frac{2GM}{R}}$ and Orbital velocity $v_o = \sqrt{\frac{GM}{R}}$.
Step 2: Meaning
We need the ratio $\frac{v_e}{v_o}$.
Step 3: Analysis
$\frac{v_e}{v_o} = \frac{\sqrt{2GM/R}}{\sqrt{GM/R}} = \sqrt{2}$.
Step 4: Conclusion
The ratio is $\sqrt{2} : 1$. Final Answer: (B)
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