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