Four identical rods are joined end to end to form asquare. The mass of each rod is M The moment ofinertia of the square about the median line isa)b)c)d)none of theseCorrect answer is option 'D'. Can you explain this answer?

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Four identical rods are joined end to end to form asquare. The mass of each rod is M The moment ofinertia of the square about the median line is

a)
b)
c)
d)
none of these

Correct answer is option 'D'. Can you explain this answer?

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Four identical rods are joined end to end to form asquare. The mass of...

To find the M.O.I of the loop about its diagonal, we use perpendicular axis theorem.

For a square, the diagonals are perpendicular to each other, and their point of intersection is the centre of the loop. Further, the two diagonals are identical, so the M.O.I about the two diagonals would be the same. Then by perpendicular axis theorem, I(centre)= 2I(diagonal). Here, I(centre) refers to the M.O.I about the axis passing through the centre of the loop, perpendicular to its plane.

Find I(centre)

The M.O.I of a rod about an axis through its centre is (ml^2)/12.

The centre of loop is at a distance (l/2) from the centre of rod, so M.O.I of 1 rod about the centre of loop is

(ml^2)/12 + m(l/2)^2 = (ml^2)/3

Now, I(centre) is the M.O.I of the 4 rods combined.

I (centre) =4*(ml^2)/3

Now we have from our first equation that

I(diagonal) = I(centre)/2

I(diagonal) =( 2/3)*ml^2

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Four identical rods are joined end to end to form asquare. The mass of each rod is M The moment ofinertia of the square about the median line isa)b)c)d)none of theseCorrect answer is option 'D'. Can you explain this answer?

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