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  4. 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 (a m b2/16). Find a.

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Q. 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 $\frac{a m b^{2}}{16}$. Find $a$.Physics Question Image

System of Particles and Rotational Motion

Solution:

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