Question

Three rods, each of mass m and length l are joined together to form a n equilateral triangle Find the moment of inertia of the system about an axis passing through its centre mass and perpendicular to the plane of the triangle.also find the radius of gyration about the same axis

Answer 1

Given, $Mass=m,length=L$

We know that,

$I=I+I+I$

$=\left(IcM\right)+m{d}^2=\frac{M{L}^2}{12}+M(\frac{L}{2\sqrt{3}}{)}^2=\frac{ML²}{12}+\frac{M{L}^2}{4\times 3}=\frac{M{L}^2}{12}+\frac{M{L}^2}{12}=\frac{2M{L}^2}{12}=\frac{M{L}^2}{6}$

$=\frac{3\times M{L}^2}{6}=\frac{M{L}^2}{2}$