Q. An ideal spring of unstretched length $'\ell '$ and force constant $'k'$ is stretched by a small length $'x'.$ It is further stretched by another small length $'y'.$ The work done in second stretching is-

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A

$\frac{1}{2}ky^{2}$

B

$\frac{1}{2}k\left(\right.x+y\left(\left.\right)^{2}$

C

$\frac{1}{2}ky\left(\right.2x+y\left.\right)$

D

$\frac{1}{2}k\left(\right.y-x\left(\left.\right)^{2}$

Solution:

$W=U_{f}-U_{i}$
$=\frac{1}{2}k\left(\right.x+y\left(\left.\right)^{2}-\frac{1}{2}kx^{2}$
$=\frac{1}{2}k\left(y^{2} + 2 x y\right)$

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