Question

The value of escape velocity \( v_e \) for a planet depends on:

• A. the mass of the body thrown from the planet
• B. the direction of projection of the body
• C. the angle of projection
• D. only on the mass of the planet
• E. its mass \( M \), density \( \rho \), and radius of the planet

Hint:

Escape velocity is independent of the mass of the object but depends on the mass and radius of the planet.

Answer 1

Answer: (E)

Step 1: The escape velocity \( v_e \) is the minimum velocity required for an object to escape the gravitational pull of the planet. 
The formula for escape velocity is: \[ v_e = \sqrt{\frac{2GM}{R}} \] where: - \( G \) is the gravitational constant,
- \( M \) is the mass of the planet,
- \( R \) is the radius of the planet.
Step 2: The escape velocity does not depend on the mass of the object being thrown, but depends on the mass \( M \) and radius \( R \) of the planet. Thus, the correct answer is that escape velocity depends on the mass, density, and radius of the planet.