(B) The rotational kinetic energy $E$ is given by $E = \frac{L^2}{2I}$,where $L$ is the angular momentum and $I$ is the moment of inertia.From this,we

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(B) The rotational kinetic energy $E$ is given by $E = \frac{L^2}{2I}$,where $L$ is the angular momentum and $I$ is the moment of inertia.From this,we can write $L = \sqrt{2IE}$.Given $I_1 = \frac{I_2}{3} \implies I_2 = 3I_1$ and $E_1 = 27E_2$.The ratio of angular momenta is $\frac{L_1}{L_2} = \frac{\sqrt{2I_1E_1}}{\sqrt{2I_2E_2}}$.Substituting the given values:$\frac{L_1}{L_2} = \sqrt{\frac{I_1}{I_2} \cdot \frac{E_1}{E_2}} = \sqrt{\frac{I_1}{3I_1} \cdot \frac{27E_2}{E_2}}$.$\frac{L_1}{L_2} = \sqrt{\frac{1}{3} \cdot 27} = \sqrt{9} = 3$.Thus,the ratio $L_1 : L_2$ is $3: 1$.

Class 11 Physics System of Particles and Rotational Motion Angular Momentum and Angular Impulse

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Two bodies rotate with kinetic energies $E_1$ and $E_2$. Their moments of inertia about their axes of rotation are $I_1$ and $I_2$. If $I_1 = \frac{I_2}{3}$ and $E_1 = 27 E_2$,then the ratio of their angular momenta $L_1$ to $L_2$ is:

MHT CET 2021 All MHT CET

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

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Class 11

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System of Particles and Rotational Motion

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Angular Momentum and Angular Impulse

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DifficultJEE MAIN 2019

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Two bodies rotate with kinetic energies $E_1$ and $E_2$. Their moments of inertia about their axes of rotation are $I_1$ and $I_2$. If $I_1 = \frac{I_2}{3}$ and $E_1 = 27 E_2$,then the ratio of their angular momenta $L_1$ to $L_2$ is:

Similar Questions

$A$ disc of mass $M$ and radius $R$ is rolling on a horizontal surface as shown in the figure. What is the magnitude of the angular momentum of the disc about the origin $O$?

$A$ particle of mass $m = 5$ is moving with a uniform speed $v = 3\sqrt{2}$ in the $XOY$ plane along the line $Y = X + 4$. The magnitude of the angular momentum of the particle about the origin is .......

$A$ particle of mass $1 \ kg$ is moving with a linear velocity of $2 \ ms^{-1}$ parallel to the positive $X$-axis. During this motion,its minimum distance from the origin is $12 \ cm$. The angular momentum of this particle about the origin is ....... $Js$.

The time dependence of the position of a particle of mass $m = 2 \ kg$ is given by $\vec r(t) = 2t \hat i - 3t^2 \hat j$. Its angular momentum with respect to the origin at time $t = 2 \ s$ is:

Consider a body,shown in the figure,consisting of two identical balls,each of mass $M$,connected by a light rigid rod of length $L$. If an impulse $J = Mv$ is imparted to the body at one of its ends,what would be its angular velocity?

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