In the set-up shown, a $200 N$ block is supported in equilibrium with the help of strings and a spring. All knotted at point $O .$ Extension in the spring is $4 cm .$ Force constant of the spring is closest to …………. $\frac{N}{m}$ . $[g = 10 m / s^{2}]$

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answer is 3000.

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Detailed Solution

In equilibrium according to Lami's theorem

$\frac{200}{\sin (180 ° - 90 °)} = \frac{T_{1}}{\sin (90 ° + 53 °)}$

$\Rightarrow \frac{200}{1} = \frac{T_{1}}{\cos (53 °)} [∵ \sin (90 ° + θ) = \cos θ]$

${\Rightarrow T}_{1} = 120 N$

$\Rightarrow Kx = 120$

$\Rightarrow K \times 0.04 = 120$

$\Rightarrow K = 3000 N / m$

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