Steel ring of radius rand cross-section area A is fitted on...

Steel ring of radius rand cross-section area $A$ is fitted on to a wooden disc of radius $R(R>r) .$ If Young's modulus be $E$, then the force with which the steel ring is expanded is:(a) $A E \frac{R}{r}$ (b) $A E \frac{(R-r)}{r}$ (c) $\frac{E(R-r)}{A} \frac{(R-r)}{r}$ (d) $\frac{E}{A} \frac{r}{R}$

Steel ring of radius rand cross-section area $A$ is fitted on to a wooden disc of radius $R(R>r) .$ If Young's modulus be $E$, then the force with which the steel ring is expanded is:(a) $A E \frac{R}{r}$
(b) $A E \frac{(R-r)}{r}$
(c) $\frac{E(R-r)}{A} \frac{(R-r)}{r}$
(d) $\frac{E}{A} \frac{r}{R}$

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Key Concepts

Young's Modulus

A material property that quantifies stiffness, defined as the ratio of stress to strain in the elastic deformation region. It helps determine how much a material will deform under a given load.

Hooke's Law

A fundamental principle in elasticity stating that, within the elastic limit of the material, the strain is directly proportional to the applied stress. This linear relationship allows us to calculate the deformation in structures like rings when subjected to forces.

Circumferential (Hoop) Strain

A specific type of strain experienced by circular objects when their radius is changed. It is calculated based on the change in circumference relative to the original circumference, which is essential in analyzing the deformation of rings.

Relationship Between Strain and Force in a Ring

Once the strain in the ring is determined, the stress can be found using Young's modulus. Multiplying this stress by the cross-sectional area gives the force required to produce the observed deformation, linking material properties to mechanical response.

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