Question

What is the value of escape velocity on the Earth's surface?

• A. \(7.9\,km/s\)
• B. \(9.8\,km/s\)
• C. \(11.2\,km/s\)
• D. \(15\,km/s\)

Hint:

Escape velocity is independent of the object's mass and depends only on the planet. For Earth: \(11.2\,km/s\), for Moon: \(2.38\,km/s\). If velocity is less than escape velocity, the object will return due to gravity.

Answer 1

The Correct Option is C

Concept: Escape velocity is the minimum velocity required for an object to escape from the gravitational field of a planet without further propulsion. The formula for escape velocity is: \[ v_e = \sqrt{\frac{2GM}{R}} \] where:
• \(G\) = gravitational constant
• \(M\) = mass of the Earth
• \(R\) = radius of the Earth

Step 1: Understand dependence on planetary parameters. Escape velocity depends only on:
• Mass of the planet
• Radius of the planet It does not depend on the mass of the object being projected.

Step 2: Substitute Earth's values. Using standard values for Earth: \[ v_e \approx 11.2\,km/s \]

Step 3: Final result. \[ \boxed{11.2\,km/s} \]