Question:
What is the formula for the escape velocity of a body from Earth's surface?
What is the formula for the escape velocity of a body from Earth's surface?
Show Hint
Escape velocity depends only on the planet's gravity and radius.
For Earth, its approximate value is $11.2\,km/s$.
Updated On: Apr 23, 2026
- $\sqrt{gR}$
- $\sqrt{2gR}$
- $\sqrt{g/2R}$
- $2gR$
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The Correct Option is B
Solution and Explanation
Concept:
Escape velocity is the minimum velocity required for an object to escape completely from the gravitational field of a planet without any further propulsion. When an object is projected upward with this velocity, it can move infinitely far away from the planet with zero final velocity. The escape velocity depends on the gravitational field strength and the radius of the planet.
Step 1: General formula for escape velocity
\[ v_e = \sqrt{\frac{2GM}{R}} \] where:
• $G$ = gravitational constant
• $M$ = mass of the Earth
• $R$ = radius of the Earth
Step 2: Using the relation $g = \frac{GM{R^2}$}
Substituting into the formula gives: \[ v_e = \sqrt{2gR} \] Conclusion:
Thus, the escape velocity of a body from Earth's surface is $\mathbf{\sqrt{2gR}}$.
Escape velocity is the minimum velocity required for an object to escape completely from the gravitational field of a planet without any further propulsion. When an object is projected upward with this velocity, it can move infinitely far away from the planet with zero final velocity. The escape velocity depends on the gravitational field strength and the radius of the planet.
Step 1: General formula for escape velocity
\[ v_e = \sqrt{\frac{2GM}{R}} \] where:
• $G$ = gravitational constant
• $M$ = mass of the Earth
• $R$ = radius of the Earth
Step 2: Using the relation $g = \frac{GM{R^2}$}
Substituting into the formula gives: \[ v_e = \sqrt{2gR} \] Conclusion:
Thus, the escape velocity of a body from Earth's surface is $\mathbf{\sqrt{2gR}}$.
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