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Answer to Question #105566 in Mechanics | Relativity for Shambhawi singh

Question #105566
A thin rectangular plate ( length=b and breath =a)is hanging with the help of two identical massless springs as shown .just after one of the spring is cut, angular acceleration of the plate is
1
2020-03-16T13:29:26-0400

As per the given question,

length and breadth of the rectangular sheet = a and b

Let the mass of the sheet is m,

Initially it was hanged with the help of two string,

so, 2T= mg

Where T is the tension in the string and g is the gravitational acceleration, α is the angular acceleration after the string breaks and I is the moment of inertia of the rectangular sheet.

Hence "T=\\dfrac{mg}{2}"

When strings breaks,

Now applying the torque equation,

"mg \\dfrac{b}{2}=I\\alpha"

"\\Rightarrow \\alpha=\\dfrac{mgb}{2I}----------------(i)"

Moment of inertia of the rectangular sheet ="\\dfrac{m(a^2+b^2)}{12}+\\dfrac{mb^2}{4}=\\dfrac{m(a^2+4b^2)}{12}"

Now substituting the of I in the equation,

"\\alpha=\\dfrac{12mgb}{2m(a^2+4b^2)}=\\dfrac{6gb}{a^2+4b^2}"

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