Solving Properties of Matter Problem: Steel Ring Expansion Force

[Amith2006]

Sir,
Please help me in solving this problem.
# A steel ring of radius r and cross sectional area A is fitted on to a wooden disc of radius R(R>r). If the Young’s modulus be Y, then what is the force with which the steel ring expands?
I just don’t have any idea on how to go about this problem.

 

[Gokul43201]

Is that the exact wording of the question ?

It is extremely ambiguous, and as such, is bordering on nonsensical.

 

[clive]

For a very small portion of the ring ($$dl=Rd \theta$$) you have the static equilibrium condition:
$$2 T sin(\frac{d \theta}{2})=N$$
where N is the force between the ring and the cylinder. Now you use
$$sin (\frac{d \theta}{2}) ~= \frac{d \theta}{2}$$
and T from the Young law for the small element $$dl$$ (when it expands between $$dl_0=r d \theta$$ and $$dl=R d\theta$$) and so on...