Question

If the value of g on a planet is 8 m/s² and its radius is 1000 m, then the value of escape velocity on that planet :
1. 1.41 km/s
2. 2.82 km/s
3. 4 km/s
4. 8 km/s

Answer 1

Correct Answer - Option 3 : 4 km/s

CONCEPT:

• Escape velocity: The minimum velocity required to escape the gravitational field of the earth is called escape velocity. 
• It is denoted by Ve.
• The escape velocity on earth is given by:

​\(\Rightarrow V = \sqrt{2gR}\)

Where g = Acceleration due to gravity, R = Radius of earth

EXPLANATION:

Given  - g = 8 m/s² and R = 1000 m

• The escape velocity of a body is given by

\(V = \sqrt{2gR}\)

\(⇒ V = \sqrt{2\times 8 \times 1000} = \sqrt{16000} =4000 m \)

\(\Rightarrow V = 4 Km\)

• Hence, option 3  is the answer