Question

A rocket is launched from the surface of Earth with a speed v0 that will allow the rocket to escape the gravitational field of Earth. The same rocket is now launched from a different planet with the same mass as Earth and four times the radius of Earth. Which of the following is a correct expression for the escape speed from the surface of the new planet?

a. 0.5V.
b. 2V0
c. 0.25v.
d. 0.71V.
e. Vo

Answer 1

option ( a ) is correct .

Step-by-step explanation:

Escape velocity on the earth = √ ( 2 GM / R )

where G is universal gravitational constant , M is mass of the earth and R is radius .

V₀ = √ ( 2 GM / R )

escape velocity on the planet where mass is equal is earth's mass and radius is 4 times that of the earth

Radius of the planet = 4 R

escape velocity of planet = √ ( 2 GM / 4R )

= .5 x √ ( 2 GM / R )

= .5 V₀

option ( a ) is correct .