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Physics - Rotation Question with Solution | TestHub

PhysicsRotationCalculation of M.I.Easy2 minPYQ_2020

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Two loops $P$ and $Q$ are made from a uniform wire. The radii of $P$ and $Q$ are $R_{1}$ and $R_{2}$ , respectively, and their moments of inertia about their axis of rotation are $I_{1}$ and $I_{2}$ , respectively. If $\frac{I_{2}}{I_{1}} = 4$ , then $\frac{R_{2}}{R_{1}}$ is

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Answer:

Solution:

$I$ of loop $= M R^{2}$

$= λ 2 π R . R^{2}$ ( $λ =$ linear mass density)

$= λ 2 π R^{3}$

$\Rightarrow \begin{matrix} I_{1} = λ 2 π R_{1}^{3} \\ I_{2} = λ 2 π R_{2}^{3} \end{matrix}\} m a d e u p o f s a m e w i r e$

$\frac{I_{2}}{I_{1}} = \frac{R_{2}^{3}}{R_{1}^{3}} = 4$

$\Rightarrow \frac{R_{2}}{R_{1}} = {(4)}^{\frac{1}{3}}$

Subject:PhysicsTopic:RotationSubtopic:Calculation of M.I.

⏱ 2mℹ️ Source: PYQ_2020

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