# Properties of matter

1. Mar 11, 2006

### Amith2006

Sir,
# 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?

2. Mar 11, 2006

### Gokul43201

Staff Emeritus
Is that the exact wording of the question ?

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

3. Mar 11, 2006

### 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....

Last edited: Mar 11, 2006