Question

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

• A. 1.2 cm
• B. 0.6 cm
• C. 0.3 cm
• D. 0.15 cm

Answer 1

Answer: (B)

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