A light elastic string has natural length L L\,L and modulus of elasticity λ\lambdaλ. It is initially stretched to an extension of yyy. The string is then stretched further until its extension is 3y3y3y, as shown below.
What is the work done against the elasticity of the string to stretch it from extension y y\,y to 3y3y3y?
2λy2L
\frac{2\lambda y^2}{L}
L2λy2
4λy2L
\frac{4\lambda y^2}{L}
L4λy2
8λy2L
\frac{8\lambda y^2}{L}
L8λy2
9λy22L
\frac{9\lambda y^2}{2L}
2L9λy2