Question

$4\,J$ of work is required to stretch a spring through $10\,cm$ beyond its unstretched length. The extra work required to stretch it through additional $10\,cm$ shall be

• A. 4 J
• B. 8 J
• C. 12 J
• D. 16 J

Answer 1

Answer: (D)

Total work done in increasing the length by $l$
$W=\frac{1}{2} \frac{Y A}{L} t^{2}$
or $W \propto l^{2}$
$\therefore \frac{W_{1}}{W_{2}}=\frac{l_{2}^{2}}{l_{2}^{2}}$
Let the initial length be $10$ .
$\frac{4}{W_{2}} =\frac{10 \times 10}{20 \times 20} $
$W_{2} =16\, J$