What Speed and Radius Conditions Keep the Hanging Mass Stationary?

[toesockshoe]

Homework Statement

A mass m on a frictionless table is attached to a hanging mass M by a cord through a hole in the table; the hole has no frictional effect on the string. Find the condition (the speed of the mass and the radius of its circular motion) with which it must spin for M to remain at rest

Homework Equations

f=ma
a_c=v^2/r

The Attempt at a Solution

is the answer v=sqrt(Mgr/m)? i feel like you need to separate r and v but I can't find a way to express both variable individually with the givens... i think speed and radius depend on each other so there can be multiple answers. is this correct?

how I solved it:

system m
x components:

Ftension = ma
Ftension = mv^2/r

system M
Fgravity - F tension (cordinate system with y-axis going downard) = ma
a is 0
so Fgravity = FtensionTENSION FORCES NEED TO BE SAME FOR BOTH SYSTEMS

so Fgravity can be rewritted as Mg
so Mg = mv^2/r
and thus v = sqrt(Mgr/m) right?[/B]

 

[haruspex]

Dimensional analysis can be used to prove there's not enough information. There's no mass dimension in either of the requested values, so the only use of the given masses is to take the ratio. That leaves you with only an acceleration (g) from which to obtain both a distance and a speed. No chance.

 

[toesockshoe]

Dimensional analysis can be used to prove there's not enough information. There's no mass dimension in either of the requested values, so the only use of the given masses is to take the ratio. That leaves you with only an acceleration (g) from which to obtain both a distance and a speed. No chance.

so is the answer i have the best i can do with the given information? i think either r or v would have to be given for me to have separate equations for both r and v... right?

 

[haruspex]

so is the answer i have the best i can do with the given information? i think either r or v would have to be given for me to have separate equations for both r and v... right?

Yes.