Question

The moment of inertia of a square lamina about the perpendicular axis through its centre of mass is $20kg{m}^2$. Then its moment of inertia about an axis touching its side and in the plane of the lamina will be:

• A. $10kg-m^2$
• B. $30kg-m^2$
• C. $40kg-m^2$
• D. $25kg-m^2$

Answer 1

The correct option is C $40kg-m^2$

L = length of square

M = mass of squqre lamina

$I_0=\frac{M{L}^2}{6}$

$20=\frac{M{L}^2}{6}$

$M{L}^2=120kg{m}^2$

By perpendicular axis Theorem and symmetry

$I_n=I_y=\frac{I_0}{2}=10kg{m}^2$

By parallel axis theorem

$I_1=I_n+M(\frac{L}{2}{)}^2$

(Here $I_1$) = Moment of Inertia about an axis touching and plane oflamina)

$I_1=10+\frac{120}{4}$

$I_1=40kg{m}^2$

Hence option (C) is correct