Mass of cylinder from hanging weight fall time

[doub]

Homework Statement

A light string is wrapped around a solid cylinder and a 300 g mass hangs from the free end of the string, as shown. When released, the mass falls a distance 54 cm in 3.0 s. Calculate the mass of the cylinder?

Homework Equations

not sure

The Attempt at a Solution

I have gotten as far as to determine the Tension on the string of -2.9N. Without known the radius of the cylinder I feel that the mass cannot be determined.

Granted these are study question but if the final is going to be like this...yikes

 

[tiny-tim]

hi doub!

A light string is wrapped around a solid cylinder and a 300 g mass hangs from the free end of the string, as shown. When released, the mass falls a distance 54 cm in 3.0 s. Calculate the mass of the cylinder?
…
Without known the radius of the cylinder I feel that the mass cannot be determined.

the motion depends on what i call the rolling mass of the cylinder, I/r², which is always half the actual mass!

carry on … you should find that the radius cancels out ​

 

[doub]

The best I can get is

$\alpha$ = (T₁ + T₂)/I

= (Fr - Tr)/1/2 mr²

= (mra -(ma+mg)r)/ 1/2 mr²

don't see how the radiii cancel each other though

 

[tiny-tim]

$\alpha$ = (T₁ + T₂)/I

= (Fr - Tr)/1/2 mr²

= (mra -(ma+mg)r)/ 1/2 mr²

sorry, i don't understand any of this

you should have an F = ma equation and a τ = Iα equation