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  4. A thin ring of an alloy of inner diameter 20 cm and cross-sectional area 1 mm 2, is heated until it easily slides on a rigid cylinder of diameter 20.025 cm. When the ring cools down, the value of tension in it is found to be a × 102 N. Find the value of a. (For alloy: .α=10-5 / ° C , Y=400 GPa )

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Q. A thin ring of an alloy of inner diameter $20 \,cm$ and cross-sectional area $1\, mm ^{2}$, is heated until it easily slides on a rigid cylinder of diameter $20.025\, cm$. When the ring cools down, the value of tension in it is found to be $a \times 10^{2} N$. Find the value of $a$.
(For alloy: $\left.\alpha=10^{-5} /{ }^{\circ} C , Y=400 \,GPa \right)$

Mechanical Properties of Solids

Solution:

$\frac{T / A}{d r / r}=Y$
$T=A Y \frac{d r}{r}=1 \times 10^{-6} \times 400 \times 10^{9} \times \frac{0.025}{20}=500\, N$