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physics question escape velocity

Hello, hoping someone could help me on this question,

The nominal escape velocity from the Earth is 11.2 km s–1. Calculate a value for the escape
velocity from a planet of mass four times that of the Earth and radius twice that of the Earth

i know we have to use v= root 2GM/R
the mark scheme says to use ratio and don't know how to go about it?

Reply 1

bored_user:)

you just multiply the top of the sqrt with 4 and the bottom with two like this:

v = √((2GM ×4)/(2×R))

And then you factor our the sqrt(4/2) and youd get sqrt(2)

So you multiply the earths escape velocity by sqrt(2) to get the escape velocity of the new planet.

And the ratio of earths escape velocity to the escape velocity of the new planet is 1/sqrt(2)