Escape velocity equation constant error in multiple choice problem

[maxelcat]

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:

 

[Orodruin]

It is not an escape velocity question. You do not require escape velocity to just orbit at a fixed radius.

 

[hutchphd]

Also you made an arithmetic error. Your answer should be wrong by √2

 

[maxelcat]

yes - found that.

 

[maxelcat]

and yes, it is not an escape velocity question. D'oh - I see that now.

Thanks