Question

Three rods each of mass 𝑚 and length $b$ form an equilateral triangle and rotate about the median of the triangle. Its moment of inertia is $\frac{am{b}^2}{16}$. Find $a$.

Answer 1

$M.I.=2\frac{m{b}^2}{3}{\sin }^2{30}^{\circ }+\frac{m{b}^2}{12}$
$=\frac{m{b}^2}{6}+\frac{m{b}^2}{12}$
$=\frac{m{b}^2}{4}=\frac{4m{b}^2}{16}$
Final Answer: $4$