Question

The minimum velocity that an object must attain to escape the gravitational force of the Earth is approximately equal to-
1. 11.2 km/h
2. 11.2 km/s
3. 11.2 m/s
4. 11.2 miles/h

Answer 1

Correct Answer - Option 2 : 11.2 km/s

The correct answer is option 2) i.e. 11.2 km/s.

CONCEPT:

• Escape velocity(Ve): The minimum velocity that an object must attain to escape the gravitational pull of the Earth is called the escape velocity.

It is given as:

Ve = √2gR

​where, g = acceleration due to gravity on the surface of the Earth, R = Radius of the Earth

EXPLANATION:

• The approximate value of acceleration due to gravity on the surface of the Earth is 9.8 m/s² or 9.8 × 10^-3 km/s².
• The approximate value of the radius of Earth is 6400 km.

V_e = √2gR

⇒ Ve = √(2 × 9.8 × 10^-3 × 6400) km/s

⇒ V_e = √125.44 km/s

⇒ V_e = 11.2 km/s

• The escape velocity of a projectile does not depend on its mass.