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If acceleration due to gravity on the surface of a planet is two times that on surface of earth and its radius is double that of earth. Then escape velocity from the surface of that planet in comparison to earth will be
  • a)
    2 Ve
  • b)
    3 Ve
  • c)
    4 Ve
  • d)
    None of these
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
If acceleration due to gravity on the surface of a planet is two times...
Acceleration due to gravity and radius

Acceleration due to gravity on the surface of a planet is directly proportional to the mass of the planet and inversely proportional to the square of its radius.

Acceleration due to gravity on the surface of the planet = 2g (where g is the acceleration due to gravity on the surface of the earth)

Radius of the planet = 2R (where R is the radius of the earth)

Escape velocity

Escape velocity is the minimum velocity required by an object to escape the gravitational pull of a planet and move into space.

Escape velocity is directly proportional to the square root of the mass of the planet and inversely proportional to the square root of its radius.

Escape velocity from the surface of the planet = Ve

Escape velocity from the surface of the earth = V

Using the formula for escape velocity:

Ve/V = √(2gR/2g(2R)) = √(R/2R) = √(1/2) = 0.707

Therefore, Ve = 0.707V

Since 0.707 is approximately equal to √(1/2), we can say that the escape velocity from the surface of the planet is approximately equal to the escape velocity from the surface of the earth multiplied by √(1/2).

Answer:

The correct option is A. The escape velocity from the surface of that planet in comparison to earth will be 2 Ve.
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