Escape velocity question - constant is wrong....

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The discussion clarifies that the question posed is not about escape velocity, as orbiting at a fixed radius does not require it. An arithmetic error was identified, leading to a correction that the answer should be adjusted by a factor of √2. Participants acknowledge the misunderstanding regarding the nature of the question. The conclusion emphasizes the importance of correctly identifying the type of physics problem being addressed. Understanding the distinction between escape velocity and orbital mechanics is crucial for accurate problem-solving.
maxelcat
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Homework Statement
A planet of mass M and radius R rotates so quickly that material at its equator only just remains on its surface.
What is the period of rotation of the planet?

This is a multiple choice question. I must be doing something wrong.9
Relevant Equations
V=-GMm/R=0.5mv^2
This is a multiple choice question. I assumed that this is an escape velocity question. I have been going round and round...
Here's what I have done:
1663239000057.png
 
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It is not an escape velocity question. You do not require escape velocity to just orbit at a fixed radius.
 
Also you made an arithmetic error. Your answer should be wrong by √2
 
yes - found that.
 
and yes, it is not an escape velocity question. D'oh - I see that now.

Thanks
 
Thread 'Chain falling out of a horizontal tube onto a table'

Thread 'Chain falling out of a horizontal tube onto a table'

My attempt: Initial total M.E = PE of hanging part + PE of part of chain in the tube. I've considered the table as to be at zero of PE. PE of hanging part = ##\frac{1}{2} \frac{m}{l}gh^{2}##. PE of part in the tube = ##\frac{m}{l}(l - h)gh##. Final ME = ##\frac{1}{2}\frac{m}{l}gh^{2}## + ##\frac{1}{2}\frac{m}{l}hv^{2}##. Since Initial ME = Final ME. Therefore, ##\frac{1}{2}\frac{m}{l}hv^{2}## = ##\frac{m}{l}(l-h)gh##. Solving this gives: ## v = \sqrt{2g(l-h)}##. But the answer in the book...
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