Question

The moment of inertia of an uniform thin sheet of mass m of the given shape about the specified axis is (axis and sheet both are in same plane):

Answer 1

answer : 7ma²/12

explanation : first of all, you should know, moment of inertia of square about an axis passing through its diagonal is like as moment of inertia of rod about an axis passing through midpoint of its length.

so, moment of inertia of square about its diagonal = ma²/12

from parallel axis theorem,

moment of inertia about the specified axis, I = moment of inertia of square about its diagonal + m(a/√2)² [ see figure ]

= ma²/12 + ma²/2

= (ma² + 6ma²)/12

= 7ma²/12

hence, moment of inertia about the specified axis is 7ma²/12 .