Question

The mass of a planet is six times that of the earth. the radius of the planet is twice that of the earth. if the escape velocity from the earth is v, then find the escape velocity from the planet is

a. √3 v
b. √2 v
c. v
d. √5 v

Answer 1

The escape velocity from a planet with mass six times that of Earth and radius twice that of Earth is √2 times the escape velocity from Earth.

Step-by-step explanation:

Escape velocity:

The escape velocity of a planet that has a mass six times that of Earth and a radius twice that of Earth is √2 times the escape velocity from Earth. To find the escape velocity from the planet, we can use the equation Vesc = √(2GM/R), where G is the gravitational constant, M is the mass of the planet, and R is the radius of the planet. Given that the mass of the planet is six times that of Earth and the radius is twice that of Earth, we can substitute these values into the equation.

To derive this, we utilize the formula for escape velocity, vesc = √(2GM/R), where G is the gravitational constant, M is the mass of the planet, and R is the radius of the planet. Given that the mass is six times greater and the radius is twice as large, we can substitute into the formula to find the new escape velocity as vnew = √(2G × 6M / 2R) = √6 × √(2GM/R) / √2 = √3 × vEarth / √2 = √2 × vEarth, which simplifies to escape velocity from the new planet being √2 × v.