Question

The escape velocity of a body depends upon mass as:

• A. \( m^0 \)
• B. \( m^1 \)
• C. \( m^2 \)
• D. \( m^3 \)

Hint:

Escape velocity is independent of the mass of the object. It only depends on the mass and radius of the planet or celestial body.

Answer 1

The Correct Option is A

Step 1: The escape velocity \( v_e \) is the minimum velocity required for a body to escape the gravitational field of a planet. It is given by the formula: \[ v_e = \sqrt{\frac{2GM}{R}}, \] where:
- \( G \) is the gravitational constant,
- \( M \) is the mass of the planet,
- \( R \) is the radius of the planet.
Step 2: As we can see, the escape velocity depends on the mass of the planet but is independent of the mass of the object escaping. The mass \( m \) of the object does not affect the escape velocity. 
Step 3: Hence, the escape velocity is independent of the mass of the object and depends only on the mass and radius of the planet.