Three point masses, each of mass 'm' are placed at the corners of an equilateral triangle of side $'…

Three point masses, each of mass 'm' are placed at the corners of an equilateral triangle of side $' \ell^{\prime}$. The moment of inertia of the system about an axis along any one side of the triangle is
  1. $\frac{1}{3} \mathrm{~m} \ell^{2}$
  2. $\frac{3}{2} \mathrm{~m} \ell^{2}$
  3. $\frac{3}{4} \mathrm{~m} \ell^{2}$
  4. $\mathrm{~m} \ell^{2}$

Solution

$O P=\sqrt{\ell^{2}-\frac{\ell^{2}}{4}}=\frac{\sqrt{3}}{2} \ell$ $\therefore \mathrm{MOI}=\mathrm{m}\left(\frac{\sqrt{3} \ell}{2}\right)^{2}=\frac{3}{4} \mathrm{~m} \ell^{2}$

Asked in: MHT CET 2020 (20 Oct Shift 1)

Practice more Rotational Motion questions on Aicharya