Question

A Square Plate Of Mass M And Side Length A Is Kept As Shown In Figure. In Equilibrium Two Of Its Side Are Horizontal And The Other Two Sides Are Vertical. What Is Its Angular Acceleration Just After Lower Spring Is Cut ?

Answer 1

Given that,

Mass = M

Side length = l

According to figure,

We need to calculate the angular acceleration

Using formula of torque

$\tau=I\alpha$

Where, I = moment of inertia

$\alpha$ = angular acceleration

So, The angular acceleration is

$F\times \dfrac{l}{2}=\dfrac{ml^2}{6}\times\alpha$

$mg\times \dfrac{l}{2}=\dfrac{ml^2}{6}\times\alpha$

$\dfrac{mgl}{2}=\dfrac{ml^2}{6}\times\alpha$

$\alpha=\dfrac{3g}{l}$

Hence, The angular acceleration is $\dfrac{3g}{l}$