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JIPMER 2019

Exam: JIPMER
Year: 2019
Subject: Physics
Chapter: Rotational Motion

JIPMER 2019 · Physics · Rotational Motion

Two disc having mass ratio 1 / 2 and diameter ratio 2 / 1 then find...

Two disc having mass ratio

1 / 2

and diameter ratio

2 / 1

then find ratio of moment of inertia.

Options

A $2: 1$
B $1: 1$
C $1: 2$
D $2: 3$

Correct answer

A. $2: 1$

Step-by-step 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}

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