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  4. When a weight of 5 kg is suspended from a copper wire of length 30 m and diameter 0.5 mm, the length of the wire increases by 2.4 cm. If the diameter is doubled, the extension produced is

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Q. When a weight of $5\, kg$ is suspended from a copper wire of length $30\, m$ and diameter $0.5\, mm$, the length of the wire increases by $2.4\, cm$. If the diameter is doubled, the extension produced is

Mechanical Properties of Solids

Solution:

$Y=\frac{M g \times 4 \times l}{\pi D^{2} \times \Delta l}$
or $\Delta l \propto \frac{1}{D^{2}}$
When $D$ is doubled, $\Delta l$ becomes one-fourth,
i.e., $\frac{1}{4} \times 2.4\, cm$,
i.e., $0.6 \,cm . \times 2.4 cm$,
i.e., $0.6\, cm$.