Spring Force and Combination of Springs questions | Spring Force and Combination of Springs jee questions

(5) $k (a - x_{0}) = 3 \Rightarrow a = \frac{3}{k} + x_{0}$ ...(i)

$k (b - x_{0}) = 2 \Rightarrow b = \frac{2}{k} + x_{0}$ ...(ii)

$Now, 3 a - 2 b = \frac{9}{k} + 3 x_{0} - \frac{4}{k} - 2 x_{0} = \frac{5}{k} + x_{0}$

$\Rightarrow {(3 a - 2 b) - x_{0}} = \frac{5}{k}$

$\Rightarrow k {(3 a - 2 b) - x_{0}} = 5$ $∴ T = 5 N$

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(3)

$k x_{1} = 5 N \Rightarrow x_{1} = \frac{5}{k}$

$k x_{2} = 7 N \Rightarrow x_{2} = \frac{7}{k}$

Then $(5 x_{1} - 2 x_{2}) k = 5 \times 5 - 2 \times 7 = 11 N$ .

(1)

$T = K (l - l_{0})$

$\Rightarrow 5 = K (1.4 - l_{0})$

$\Rightarrow 7 = K (1.56 - l_{0})$

$\Rightarrow \frac{5}{1.4 - l_{0}} = \frac{7}{1.56 - l_{0}}$

$∴ l_{0} = 1 m$

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