Question

A spring force constant $k$ is cut in two parts at its one third length. when both the parts are streatched by same amount. The work done is

• 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

Let the length of spring be ${}^{\prime }{l}^{\prime }$ m
Length of one part of a spring $=\frac{l}{3}$$\text{m}$ (shorter part)
Length of other part of spring $=\frac{2l}{3}$$\text{m}$ . (longer part)
$\because$ Spring constant is inversely proportional to the length of spring and workdone by the spring $=\frac{1}{2}k{x}^2$

More work is done by the spring with more spring constant

$\therefore$ The work done is greater for the shorter part