A uniform square plate of mass m is supported with its plane vertical as shown in the figure. Assume the centre of mass is on a horizontal line passing through A . If the cable at B breaks then just a

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A uniform square plate of mass m is supported with its plane vertical as shown in the figure. Assume the centre of mass is on a horizontal line passing through A . If the cable at B breaks then just after that the angular acceleration of the plate is

TestHub · Accepted Answer

The plate will rotate about the hinged point ( point $A$ ) after breaking of the cable

$∴$ using $τ = Iα$ for the plate

$Mg \frac{b}{\sqrt{2}} = \frac{2}{3} {Mb}^{2} α$ ( Moment of inertia about point $A$ is $\frac{{Mb}^{2}}{6} + M {(\frac{b}{\sqrt{2}})}^{2} = \frac{2}{3} {Mb}^{2}$ )
$∴ α = \frac{3 g}{2 \sqrt{2} b}$

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