Calculation of Moment of Inertia of Circle and Square

To calculate the ratio of moment of inertia of circle and square having same area about their centriodal axis, we need to first calculate the moment of inertia of circle and square.

Moment of Inertia of a Circle about its Centroidal Axis

The moment of inertia of a circle about its centroidal axis is given by the formula:

I = (πr^4)/4

where r is the radius of the circle.

Moment of Inertia of a Square about its Centroidal Axis

The moment of inertia of a square about its centroidal axis is given by the formula:

I = (a^4)/12

where a is the length of one side of the square.

Ratio of Moment of Inertia of Circle and Square

Now, we can calculate the ratio of moment of inertia of circle and square having same area about their centriodal axis by substituting the values of moment of inertia of circle and square in the following formula:

Ratio = (Moment of Inertia of Circle)/(Moment of Inertia of Square)

= [(πr^4)/4]/[(a^4)/12]

= (3/π)(r/a)^4

As the circle and square have the same area, we can write:

πr^2 = a^2

Therefore, (r/a)^2 = 1/π

Substituting this value in the above formula, we get:

Ratio = (3/π) x (1/π)^2

= 3/π^3

Hence, the ratio of moment of inertia of circle and square having same area about their centriodal axis is 3/π.

Answer: (A) 3/π

The correct option is A