Q. Two rods of equal mass ```m` and length `l` lie along the x-axis and y-axis with their centres origin.What is the moment of inertia of both about the line x=y. A) `(ml^2)/3` B) `(ml^2)/4` C)...

Q. Two rods of equal mass ```m` and length `l` lie along the x-axis and y-axis with their centres origin.What is the moment of inertia of both about the line x=y.

A) `(ml^2)/3`

B) `(ml^2)/4`

C) `(ml^2)/12`

D) `(ml^2)/6`

Asked on by user8235304

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valentin68 | College Teacher | (Level 3) Associate Educator

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We will compute the moment of inertia with respect to x axis since the other moment of inertia will be the same.By definition the moment of inertia of a body with respect to an axis is

`I = sum_(i)(r_i^2*m_i)` where the summation is performed for all i parts that compose the body.

The rod situated along the x axis will not give any contribution to the moment of inertia since for it, all `r_i =0` .

For the rod situated along the y axis we have the linear density of mass

`lambda = m/l`

and by the above definition we can write

`I_x = int_(-l/2)^(+l/2)y^2*dm = int_(-l/2)^(+l/2)y^2*(m/l)*dy =`

`= (m/l)*y^3/3 ((-l/2)->(+l/2)) = (m/(3*l))*(l^3/8+l^3/8) =(1/12)m*l^2 `

The correct answer is C) `(m*l^2)/12`

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