A spring of force constant K is first stretch | vedclass

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(C) The work done in stretching a spring by a distance $x$ is given by the potential energy stored,$U = \frac{1}{2} K x^2$.Initial work done to stretc

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$\frac{1}{2} K b(2 a+b)$

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(C) The work done in stretching a spring by a distance $x$ is given by the potential energy stored,$U = \frac{1}{2} K x^2$.Initial work done to stretch the spring by distance $a$ is $W_1 = \frac{1}{2} K a^2$.Total work done to stretch the spring by a total distance of $(a+b)$ is $W_2 = \frac{1}{2} K (a+b)^2$.The work done in stretching the spring further by distance $b$ is the difference between the total work and the initial work:$\Delta W = W_2 - W_1$$\Delta W = \frac{1}{2} K (a+b)^2 - \frac{1}{2} K a^2$$\Delta W = \frac{1}{2} K (a^2 + 2ab + b^2 - a^2)$$\Delta W = \frac{1}{2} K (2ab + b^2)$$\Delta W = \frac{1}{2} K b(2a + b)$.

$A$ spring of force constant $K$ is first stretched by distance $a$ from its natural length and then further by distance $b$. The work done in stretching the part $b$ is .............

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