What is the escape velocity from the surface of a planet with a radius of 3R and

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Question: What is the escape velocity from the surface of a planet with a radius of 3R and mass 4M?

Options:

Correct Answer: √(8GM/R)

Solution:

Escape velocity v = √(2GM/R); here, v = √(2 * 4GM / 3R) = √(8GM/3R).

What is the escape velocity from the surface of a planet with a radius of 3R and mass 4M?

What is the escape velocity from the surface of a planet with a radius of 3R and mass 4M?

Step 1: Understand the formula for escape velocity, which is v = √(2GM/R). Here, G is the gravitational constant, M is the mass of the planet, and R is the radius of the planet.
Step 2: Identify the values given in the question. The radius of the planet is 3R and the mass is 4M.
Step 3: Substitute the values into the escape velocity formula. Replace M with 4M and R with 3R in the formula: v = √(2 * G * (4M) / (3R)).
Step 4: Simplify the equation. This gives us v = √(8GM / 3R).
Step 5: The final expression for escape velocity from the surface of the planet is v = √(8GM / 3R).

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