Question

Four particles of mass 1g, 2g, 3g, and 4g are at 1cm, 2cm, 3cm and 4cm from the axis of rotation respectively then the moment of inertia of the system in g-cm ${}^2$ is

• A. 63
• B. 100
• C. 36
• D. 48

Answer 1

The correct option is B 100

$\begin{array}{c}\text{Let, particles be}A,B,C\text{and}D\text{.}\\ \text{Given,}{m}_A=1g,m_B=2g,m_c=3g\text{and}{m}_D=4g\\ \text{and,}{r}_A=1cm,m_B=2cm,m_c=3cm\text{and}{m}_D=4cm.\end{array}$

$\begin{array}{c}\text{Thus, moment of inertia of system}={\sum }_{i=A}^D{m}_i{r}_i^2\\ =(1\times 1)+(2\times 4)+(3\times 9)+(4\times 16)g{cm}^2\\ =100g{cm}^2\end{array}$