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

AI Thread Summary
The discussion revolves around a multiple-choice question regarding the escape velocity from the Moon, specifically whether the answer is 4/81 v(esc). Participants emphasize the importance of showing work before receiving guidance, urging the original poster to explain their reasoning. They suggest calculating the escape velocity of the Moon and checking it against known values to verify correctness. Additionally, there is a recommendation to simplify the problem by using distinct symbols for different variables to avoid confusion. The conversation highlights the need for careful algebraic manipulation and understanding of the concepts involved.
jellybean-spider
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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... :cry:
 
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√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)
 
jellybean-spider said:
√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?
 
jellybean-spider said:
√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.
 
jellybean-spider said:
√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.
 
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