(D) Given that the rotational kinetic energies are equal:$(K.E.)_A = (K.E.)_B$$\frac{1}{2} I_1 \omega_1^2 = \frac{1}{2} I_2 \omega_2^2$$\frac{I_1}{I_2

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(D) Given that the rotational kinetic energies are equal:$(K.E.)_A = (K.E.)_B$$\frac{1}{2} I_1 \omega_1^2 = \frac{1}{2} I_2 \omega_2^2$$\frac{I_1}{I_2} = \frac{\omega_2^2}{\omega_1^2} \implies \frac{\omega_2}{\omega_1} = \sqrt{\frac{I_1}{I_2}} \quad ...(i)$Also,rotational kinetic energy is given by $K.E. = \frac{L^2}{2I}$. Since kinetic energies are equal:$\frac{L_1^2}{2I_1} = \frac{L_2^2}{2I_2}$$\frac{I_2}{I_1} = \frac{L_2^2}{L_1^2}$Given the ratio of angular momenta $\frac{L_1}{L_2} = \frac{1}{\sqrt{3}}$,we have $\frac{L_2}{L_1} = \sqrt{3}$.Therefore,$\frac{I_2}{I_1} = (\sqrt{3})^2 = 3$.Thus,$I_2 = 3 I_1$.

Class 11 Physics System of Particles and Rotational Motion Rotational Kinetic Energy

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Two bodies $A$ and $B$ have their moments of inertia $I_1$ and $I_2$ respectively about their axis of rotation. If their kinetic energies of rotation are equal and their angular momenta $L_1$ and $L_2$ respectively are in the ratio $1 : \sqrt{3}$,then $I_2$ will be

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A
$\frac{1}{3} I_1$
B
$\sqrt{3} I_1$
C
$2 I_1$
D
$3 I_1$

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Class 11

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System of Particles and Rotational Motion

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Rotational Kinetic Energy

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$A$ flywheel rotating about a fixed axis has a kinetic energy of $360 \ J$ when its angular speed is $30 \ rad/s$. The moment of inertia of the wheel about the axis of rotation is ...... $kg \ m^2$.

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$A$ body rotating with an angular velocity of $3 \ rad/s$ has a moment of inertia of $3 \ kg \cdot m^2$ about its axis of rotation. The rotational kinetic energy of this body is equal to the translational kinetic energy of another body of mass $27 \ kg$. The speed of the $27 \ kg$ mass body is .......... $m/s$.

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If $L, M$,and $P$ are the angular momentum,mass,and linear momentum of a particle respectively,which of the following represents the kinetic energy of the particle when the particle rotates in a circle of radius $R$?

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In the given figure,two wheels $P$ and $Q$ are connected by a belt $B$. The radius of $P$ is three times as that of $Q$. In case of same rotational kinetic energy,the ratio of rotational inertias $\left(\frac{I_{P}}{I_{Q}}\right)$ will be $x: 1$. The value of $x$ will be $.....$ .

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Three particles are situated on a light and rigid rod along the $Y$-axis as shown in the figure. If the system is rotating with an angular velocity of $2 \, rad/s$ about the $X$-axis,then the total kinetic energy of the system is ...... $J$.

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Two bodies $A$ and $B$ have their moments of inertia $I_1$ and $I_2$ respectively about their axis of rotation. If their kinetic energies of rotation are equal and their angular momenta $L_1$ and $L_2$ respectively are in the ratio $1 : \sqrt{3}$,then $I_2$ will be

Similar Questions

$A$ flywheel rotating about a fixed axis has a kinetic energy of $360 \ J$ when its angular speed is $30 \ rad/s$. The moment of inertia of the wheel about the axis of rotation is ...... $kg \ m^2$.

If $L, M$,and $P$ are the angular momentum,mass,and linear momentum of a particle respectively,which of the following represents the kinetic energy of the particle when the particle rotates in a circle of radius $R$?

In the given figure,two wheels $P$ and $Q$ are connected by a belt $B$. The radius of $P$ is three times as that of $Q$. In case of same rotational kinetic energy,the ratio of rotational inertias $\left(\frac{I_{P}}{I_{Q}}\right)$ will be $x: 1$. The value of $x$ will be $.....$ .

Three particles are situated on a light and rigid rod along the $Y$-axis as shown in the figure. If the system is rotating with an angular velocity of $2 \, rad/s$ about the $X$-axis,then the total kinetic energy of the system is ...... $J$.

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