Question

When a weight of $10kg$ is suspended from a copper wire of length $3m$ and diameter $0.4mm$. its length increases by $2.4cm$. If the diameter of the wire is doubled, then the extension in its length will be______

• A. 9.6 cm
• B. 4.8 cm
• C. 1.2 cm
• D. 0.6 cm

Answer 1

Answer: (D)

Mass of the suspended body, $m=10kg$
Length of copper wire, $l=3m$
Diameter, $d=0.4mm$
$\therefore$ Radius,
$r=\frac{d}{2}=\frac{0.4}{2}=0.2mm=2\times 10^{-4}m$
Increased length, $\Delta l=2.4cm=2.4\times 10^{-2}m$
Young's modulus of the wire is given as
$Y=\frac{mgl}{\pi r^2\Delta l}=\frac{10\times 10\times 3}{\pi \times {\left(2\times 10^{-4}\right)}^2\times 2.4\times 10^{-2}}$
$=\frac{300}{3\times 10^{-9}}=10^{11}N/m^2$
When $d^{\prime }=2d=2\times 0.4=0.8mm$
$r=\frac{d^{\prime }}{2}=\frac{0.8}{2}=0.4mm=4\times 10^{-4}m$
Hence, $\Delta l=\frac{mgl}{\pi r^{2}Y}=\frac{10\times 10\times 3}{\pi \times {\left(4\times 10^{-4}\right)}^2\times 10^{11}}$
$=5.96\times 10^{-3}m=0.596cm\simeq 0.6cm$