All the surfaces shown in the figure are smooth. System is released with the spring unstretched. In equilibrium, compression in the spring will be

All the surfaces shown in the figure are smooth. System is released with the spring unstretched.
In equilibrium, compression in the spring will be

A
$\frac{mg}{\sqrt{2} k}$
B
$\frac{2mg}{k}$
C
$\frac{(M + m) g}{\sqrt{2} k}$
D
$\frac{mg}{k}$

Solution:

$N \cos θ = mg; N \sin θ = k x; \tan θ = \frac{k x}{mg} ∴ θ = 45 ° \Rightarrow k x = mg ∴ x = \frac{mg}{k}$

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