Q112 / 180 · JIPMER 2019 · Physics

Two disc having mass ratio $1 / 2$ and diameter ratio $2 / 1$ then find ratio of moment of inertia.

  • Correct answer
    A
    $2: 1$
  • B
    $1: 1$
  • C
    $1: 2$
  • D
    $2: 3$

Solution

Given, mass ratio of two disc $\mathrm{m}_1: \mathrm{m}_2=1: 2 \text { i.e. } \frac{\mathrm{m}_1}{\mathrm{~m}_2}=\frac{1}{2}$ and diameter ratio $\frac{\mathrm{d}_1}{\mathrm{~d}_2}=\frac{2}{1} \Rightarrow \frac{\mathrm{r}_1}{\mathrm{r}_2}=\frac{2}{1}$ $\therefore$ Ratio of their moment of inertia, $\begin{array}{ll} \quad \frac{\mathrm{I}_1}{\mathrm{I}_2}= & \frac{\frac{\mathrm{m}_1 \mathrm{r}_1^2}{2}}{\frac{\mathrm{m}_2 \mathrm{r}_2^2}{2}}=\frac{\mathrm{m}_1}{\mathrm{~m}_2} \cdot\left(\frac{\mathrm{r}_1}{\mathrm{r}_2}\right)^2=\frac{1}{2}\left(\frac{2}{1}\right)^2=\frac{2}{1} \\ \therefore \quad \mathrm{I}_1: \mathrm{I}_2=2: 1 \end{array}$

Hence, the correct answer is option: 'A'.

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