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.
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`