Question

A spring of force constant k is cut in two parts at its one-third length. When both the parts are stretched by same amount. The work done in the two parts will be:
(Note- Spring constant of a spring is inversely proportional to length of spring.)

• A. equal in both
• B. greater for the longer part
• C. greater for the shorter part
• D. data insufficient

Answer 1

The correct option is C greater for the shorter part

As we know that spring constant k is inversely proportional to length of spring

$k\alpha \frac{1}{L}$

work done = change in potential energy

$workdone=\Delta PE=\frac{1}{2}k{x}^2$

so work done is directly proportional to k

it work done is inversely proportional to length

$workdone\alpha k\alpha \frac{1}{L}$

hence work done is more for small length of spring as compared to larger.