Question

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