Fields (Gravitational fields) -- Escape Velocity from the Moon

[jellybean-spider]

Homework Statement

The escape velocity for an object at the surface of the Earth is V(esc). The diameter of the moon is 4 times smaller than that of the Earth and the mass of the Moon is 81 times smaller than that of the Earth. What is the escape velocity of the object on the moon.

Relevant Equations

V(esc) = sqrt (2GM/R)

It's an MCQ, and I chose 4/81 v(esc). Is this correct? There isn't a marking scheme...

 

[Steve4Physics]

Hi @jellybean-spider. Welcome to PF.

The rules here require you to show evidence of your own effort before we offer any guidance. See https://www.physicsforums.com/threads/homework-help-guidelines-for-students-and-helpers.686781/

So you first need to explain how/why you chose '4/81 v(esc)'.

 

[jellybean-spider]

√2G(1/81)M/(1/4)r = √2GM/r

This is with the information that I have got from the question and then I think using proportionality I got 4/81 v(sec)

 

[PeroK]

√2G(1/81)M/(1/4)r = √2GM/r

This is with the information that I have got from the question and then I think using proportionality I got 4/81 v(sec)

Why don't you calculate the escape velocity of the Moon from that and check online to see whether you are right?

 

[Steve4Physics]

√2G(1/81)M/(1/4)r = √2GM/r

Check your algebra. If you cancel √(GM/r) from both sides of your equation you are left with:
√(1/81)/(1/4)) = 1
which should sound (loud) alarm bells!

Hint: for practice/understanding, first solve a simple example:
If y=√x, what happens to y if, say, x increases by a factor of 25?

Then try the problem again. Don't forget to check your answer makes sense as suggested by by@PeroK.

 

[haruspex]

√2G(1/81)M/(1/4)r = √2GM/r

This is with the information that I have got from the question and then I think using proportionality I got 4/81 v(sec)

It is too confusing using the same symbol for different variables. Add subscripts ($M_e, M_m$ for Earth and Moon, etc.) or use different case (M, m, R, r) or different letters.