Question

# A steel ring of radius $$r$$ and cross sectional area $$A$$ is fitted onto a wooden disc of radius $$R(R>r)$$. If the Young's modulus of steel is $$Y$$, then the force with which the steel ring is expanded is

A
AY(R/r)
B
AY(Rr)/r
C
(Y/A)[(Rr)/r]
D
Yr/AR

Solution

## The correct option is B $$AY(R-r)/r$$Let $$T$$ be the tension in the ring, then $$Y=\displaystyle\frac{T.2\pi r}{A.2\pi(R-r)}=\frac{Tr}{A(R-r)}$$$$\therefore T=\displaystyle\frac{YA(R-r)}{r}$$Physics

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