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5.Work, Energy, Power and Collision
normal
The length of a spring is $\alpha $ when a force of $4\,N$ is applied on it and the length is $\beta $ when $5\,N$ force is applied. Then the length of spring when $9\,N$ force is applied is
A
$5\beta -4\alpha $
B
$\beta -\alpha $
C
$5\alpha -4\beta $
D
$9(\beta - \alpha )$
Solution

Let the natural length of the spring $=\ell_{0}$
From figure
$4=\mathrm{k}\left(\alpha-\ell_{0}\right) \ldots(\mathrm{i})$
$5=\mathrm{k}\left(\beta-\ell_{0}\right) \dots(\mathrm{ii})$
$9=\mathrm{k}\left(\gamma-\ell_{0}\right) \ldots(\mathrm{iii})$
eq. $\frac{(\mathrm{iit})-(\mathrm{i})}{(\mathrm{ii})-(\mathrm{i})} \Rightarrow \frac{5}{4}=\frac{\mathrm{k}(\gamma-\alpha)}{\mathrm{k}(\gamma-\beta)}$
$\gamma=5 \beta-4 \alpha$
Standard 11
Physics