Question

A weight suspended from the free end of a vertically hanging spring produces an extension of $3$ cm. The spring is cut into two parts so that the length of the longer part is ${\frac{2}{3}}^{rd}$ of the original length, If the same weight is now suspended from the longer part of the spring, the extension produced will be

• A. 0.1 cm
• B. 0.5 cm
• C. 1 cm
• D. 2 cm

Answer 1

The correct option is D 2 cm

Initially, $3k=mg$ or $k=\frac{mg}{3}$
New force constant of longer part
$k{}^{\prime }=\frac{3}{2}k=\frac{3}{2}\times \frac{mg}{3}=\frac{mg}{2}$
Finally, $k{}^{\prime }y=mg$
$y=\frac{mg}{k{}^{\prime }}=\frac{mg}{mg}\times 2=2cm$