Question

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 1

Final Answer : $40 kg/m^2$

Steps:
1) We have,

L => Length of square
M = > Mass of Square Lamina
$I_{o} = \frac{ML^2}{6} \\ => 20 = \frac{ML^2}{6} \\ => ML^2 = 120 kg m^2$

2) By Perpendicular axes Theorem and Symmetry,
$I_x = I_y = \frac{I_{o}}{2} =10kg m^2$

3) By Parallel axes Theorem,
$I_1 = I_x +M( \frac{L}{2} )^2 \\ => I_1 = 10+ \frac{120}{4} \\ => I_1 = 10+ 30 = 40kg m^2$

Hence, Moment of Inertia about an axis touching it's side in the plane of Lamina is $40kg m^2$

Answer 2

Answer:

I = ml²/6

20=ml²/6

ml²=120kgm²

Ix=Iy=I/2=10kgm²

I1=Ix+ m(l/2)²

I1=10+120/4

I1=10+30=40kgm²