The moment of inertia of a square lamina about the perpendicular axis through its centre of mass is 20 kg per metre square then its moment of inertia about an axis touching its side and in the plane of the lamina will be

Answer:

Given parameters

Moment of inertia of a square lamina about the perpendicular axis at the center of the square (I0) = 20 kgm-2

Let us consider

L = Length of square

M = Mass of the square lamina

\(\begin{array}{l}I_{0}= \frac{ML^{2}}{6}\end{array} \)

20 = ML2/6

ML2 = 120 kgm2

According to the parallel axis theorem

Ix = Iy = I0/2= 10kgm-2

I1 = Ix + M(L/2)2

⇒ I1 = Ix + ML2/4

⇒ I1 = 10 + 120/4

⇒ I1 = 40 kgm-2

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