Question

The value of escape velocity of a body from the Earth's surface is Vₑₛc =

• A. √((GM)/(R))
• B. 2√((GM)/(R))
• C. √((2GM)/(R))
• D. √((GM)/(2R))

Hint:

The escape velocity depends on the mass of the Earth and the distance from the center of the Earth (or the celestial body).

Answer 1

The Correct Option is C

The escape velocity is the minimum speed an object must have to escape the gravitational pull of the Earth (or any celestial body) without any additional propulsion. The formula for escape velocity is derived from the law of conservation of energy. The formula for escape velocity from the Earth's surface is given by: Vₑₛc = √((2GM)/(R)) Where:
- G is the gravitational constant,
- M is the mass of the Earth,
- R is the radius of the Earth.
• (A) √((GM)/(R)): Incorrect. This is not the correct formula for escape velocity. • (B) 2√((GM)/(R)): Incorrect. This formula does not represent the escape velocity. • (C) √((2GM)/(R)): Correct. This is the correct formula for escape velocity. • (D) √((GM)/(2R)): Incorrect. This does not represent escape velocity either. Thus, the correct value of the escape velocity is √((2GM)/(R)), as given in option (C). Final Answer: (C) √((2GM)/(R)).