Question

For a uniform rectangular sheet shown in the figure, the ratio of moments of inertia about the axes perpendicular to the sheet and passing through O (the centre of mass) and O' (corner point) is 

(1) 1/2 

(2) 1/4 

(3) 1/8 

(4) 2/3

Answer 1

Answer is (2) 1/4

Answer 2

Option B is ans

Calculate moment of inertia passing through Point O then calculate MOI passing through O' and then divide both and get the ans

Answer 3

The correct option is B)1/4

Step-by-Step Explanation!!

Step 1: Given data

Length of the rectangle (l) = 80 cm

The breadth of the rectangle (b) = 60 cm

Moment of inertia = I

Moment of inertia about the axis perpendicular to the sheet and passing through O = I_O

Moment of inertia at the point O' =I_O'

Total mass = M

Step 2: To find the ratio of moment of inertia

We know

I_O = (M/12)(l²+b²)

I_O = (M/12)(80²+60²)

Using the Parallel axis theorem

I_O' = I_O + (M)((b/2)²+(l/2)²)

        = (Ml²/12)+(Mb²/12)+(Ml²/4)+(Mb²/4)

I_O' = (M/12)(l²+b²)+M((l²/4)+(b²/4))

I_O' = I_O + M(50²)

Then the ratio of moment of inertia

(I_O/I_O') = ((M/12)(10000)/(M/12)(10000) + M(2500)

                 = (1/4)

Hence the ratio of moment of inertia (I_O/I_O') = 1/4

Therefore the correct answer is Option B)1/4

Please select my answer as the Best!!!

I will surely help you next time if you need any help..

Thank you!!!