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Physics - Rotation Question with Solution | TestHub

PhysicsRotationMiscellaneousEasy2 minPYQ_2020

PhysicsEasysingle choice

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 are $I_{1}$ and $I_{2}$ respectively. If $I_{2} = 4 I_{1}$ , then $\frac{r_{2}}{r_{1}}$ equals

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Answer:

Solution:

Moment of inertia of a loop is,

$I = M r^{2} = (2 π r A ρ) r^{2}$

Therefore $I \propto r^{3}$

or $r \propto I^{\frac{1}{3}}$

For the two loops

$\frac{r_{2}}{r_{1}} = {(\frac{I_{2}}{I_{1}})}^{\frac{1}{3}}$

As $I_{2} = 4 I_{1}$

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

Stream:NTA_ABHYAS_NEETSubject:PhysicsTopic:RotationSubtopic:Miscellaneous

⏱ 2mℹ️ Source: PYQ_2020

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