A bead of mass 5 kg is free to slide on the horizontal rod AB . They are connected to two identical springs of natural length h ms. As shown. If initially bead was at O&M is vertically below L then, velocity of bead at point N will be x h m/s then x= ___________

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A bead of mass 5 kg is free to slide on the horizontal rod $A B$ . They are connected to two identical springs of natural length $h$ ms. As shown. If initially bead was at $O & M$ is vertically below $L$ then, velocity of bead at point $N$ will be $x h m/s$ then $x =$ ____________

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answer is 5.

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Detailed Solution

Let the length of the spring = $l$
$l = \frac{h}{\cos 37} = \frac{5 h}{4}$
Extension in spring $x = l - h = \frac{h}{4}$
$\frac{1}{2} k x^{2} + \frac{1}{2} k x^{2} = \frac{1}{2} m v^{2}$
$2 \times \frac{1}{2} \times 1000 \times \frac{h^{2}}{16} = \frac{1}{2} 5 v^{2}$
$v^{2} = 25 h^{2} \Rightarrow v = 5 h m / s^{2}$