Question

When the load on a wire is increased from $3kg$ $wt$ to $5kg$ $wt$ the elongation increases from $0.61mm$ to $1.02mm$. The required work done during the extension of the wire is:

• A. $16\times {10}^{-3}J$
• B. $8\times {10}^{-2}J$
• C. $20\times {10}^{-2}J$
• D. $11\times {10}^{-3}J$

Answer 1

Answer: (A)

$16\times {10}^{-3}J$

Given:

Apply Load: $M_1=3kg\Delta L=0.61mm{M}_2=5kg\Delta L=1.02mm$

Work done is stretching the wire through $0.61mm$ under the load of $3kg$ $wt$
$W_1=\frac{1}{2}stretchingforce\times extension=\frac{1}{2}\times 3\times 9.8\times 0.61\times {10}^{-3}=8.967\times {10}^{-3}J$
Work done in stretching the wire through $1.02mm$ under the load of $5kg$ $wt$
$W_2=\frac{1}{2}\times 5\times 9.8\times 1.02\times {10}^{-3}=24.99\times {10}^{-3}J$
Hence work done in stretching the wire from $0.61mm$ to $1.02mm$
$\Delta W=W_2-W_1=(24.99-8.961)\times {10}^{-3}\simeq 16\times {10}^{-3}J$