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PART - 1 CH - 5Work, Energy and Power — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysicsPART - 1 CH - 5Work, Energy and Power2 Marks
Question
If the force constant of two springs are $k_1$ and $k_2$ respectively and $k_1=2 k_2$ then find the ratio of work done on pulling those springs by applying equal force.
✓

Answer

Here,
$ \begin{aligned} k_1 & =2 k_2 \\ F_1 & =F_2 \\ -k_1 x_1 & =-k_2 x_2 \end{aligned} $
or
$ \begin{array}{l} \frac{x_1}{x_2}=\frac{k_2}{k_1} \\ \frac{x_1}{x_2}=\frac{k_2}{2 k_2} \quad \because k_1=2 k_2 \end{array} $
or
$ \frac{x_1}{x_2}=\frac{1}{2} $
and
$ \begin{aligned} \frac{W_1}{W_2} & =\frac{-\frac{1}{2} k_1 x_1^2}{-\frac{1}{2} k_2 x_2^2} \\ & =\frac{2 k_2}{k_2} \times\left(\frac{x_1}{x_2}\right)^2=\frac{2 k_2}{k_2} \times \frac{1}{4} \\ \frac{W_1}{W_2} & =\frac{1}{2} \\ W_1: W_2 & =1: 2 \end{aligned} $

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