Question

Three point masses $m_1,m_2$ and $m_3$ are located at the vertices of an equilateral triangle of side ${}^{\prime }{a}^{\prime }$. What is the moment of inertia of the system about an axis along the altitude of the triangle passing through $m_1$?

• A. $(m_1+m_2)\frac{a^2}{4}$
  
• B. $(m_2+m_3)\frac{a^2}{4}$
• C. $(m_1+m_3)\frac{a^2}{4}$
• D. $(m_1+m_2+m_3)\frac{a^2}{4}$

Answer 1

The correct option is B $(m_2+m_3)\frac{a^2}{4}$


Moment of Inertia od discrete bodies is $\sum m{r}^2$
$I=m_3{\left(\frac{a}{2}\right)}^2+m_2{\left(\frac{a}{2}\right)}^2$
$I=(m_2+m_3)\frac{a^2}{4}$