MHT CET · Physics · Rotational Motion
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
- A \(\frac{1}{3} \mathrm{~m} \ell^{2}\)
- B \(\frac{3}{2} \mathrm{~m} \ell^{2}\)
- C \(\frac{3}{4} \mathrm{~m} \ell^{2}\)
- D \(\mathrm{~m} \ell^{2}\)
Answer & Solution
Correct Answer
(C) \(\frac{3}{4} \mathrm{~m} \ell^{2}\)
Step-by-step Solution
Detailed explanation
\(O P=\sqrt{\ell^{2}-\frac{\ell^{2}}{4}}=\frac{\sqrt{3}}{2} \ell\)
\(\therefore \mathrm{MOI}=\mathrm{m}\left(\frac{\sqrt{3} \ell}{2}\right)^{2}=\frac{3}{4} \mathrm{~m} \ell^{2}\)
\(\therefore \mathrm{MOI}=\mathrm{m}\left(\frac{\sqrt{3} \ell}{2}\right)^{2}=\frac{3}{4} \mathrm{~m} \ell^{2}\)
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