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 initial speed an object must have to break free from the gravitational pull of a massive body (like a planet) and never return.
Step 1: Understanding the Question:
We need the numerical value of escape velocity specifically for Earth's surface.
Step 2: Key Formula or Approach:
The formula for escape velocity (\(v_e\)) is derived from conservation of energy:
\[ v_e = \sqrt{\frac{2GM}{R}} = \sqrt{2gR} \]
Where:
- \(G\) = Gravitational constant
- \(M\) = Mass of Earth
- \(R\) = Radius of Earth
- \(g\) = Acceleration due to gravity (\(\approx 9.8\,m/s^2\))
Step 3: Detailed Solution:
1. Radius of Earth \(R \approx 6.4 \times 10^6 \, m\).
2. Acceleration due to gravity \(g \approx 9.8 \, m/s^2\).
3. Calculation:
\[ v_e = \sqrt{2 \times 9.8 \times 6.4 \times 10^6} \]
\[ v_e \approx 11200 \, m/s = 11.2 \, km/s \]
Step 4: Final Answer:
The escape velocity on Earth's surface is 11.2 km/s.