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  4. A uniform rod <m:omath><m:r></m:r></m:omath> AB of mass <m:omath><m:r></m:r></m:omath> m is suspended in equilibrium from two similar springs as shown. If spring <m:omath><m:r></m:r></m:omath> 2 breaks, then the angular acceleration of the bar at that instant will be <img class=img-fluid question-image alt=Question src=https://cdn.tardigrade.in/q/nta/p-0t3kxk0c1f8dytee.jpg />

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Q. A uniform rod $AB$ of mass $m$ is suspended in equilibrium from two similar springs as shown. If spring $2$ breaks, then the angular acceleration of the bar at that instant will be
Question

NTA AbhyasNTA Abhyas 2022

Solution:

Solution
$m$ equilibrium
$2kxsin30^{o}=mg$
$kx=mg\ldots \left(i\right)$
When spring is snapped
Equation of rotation motion about COM.
$kx\cdot sin30^{o}\frac{l}{2}=Iα$
$=\frac{ml^{2}}{12}\alpha \Rightarrow \alpha =\frac{3 g}{l}$