(C) The moment of inertia $I$ of the system about the axis passing through the midpoint is given by $I = m(\frac{d}{2})^2 + m(\frac{d}{2})^2 = 2m(\fra

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$\frac{2}{d} \sqrt{\frac{K}{m}}$

(C) The moment of inertia $I$ of the system about the axis passing through the midpoint is given by $I = m(\frac{d}{2})^2 + m(\frac{d}{2})^2 = 2m(\frac{d^2}{4}) = \frac{md^2}{2}$.Rotational kinetic energy is given by $K = \frac{1}{2} I \omega^2$.Substituting the value of $I$,we get $K = \frac{1}{2} (\frac{md^2}{2}) \omega^2 = \frac{md^2 \omega^2}{4}$.Rearranging for $\omega^2$,we get $\omega^2 = \frac{4K}{md^2}$.Taking the square root on both sides,we get $\omega = \sqrt{\frac{4K}{md^2}} = \frac{2}{d} \sqrt{\frac{K}{m}}$.

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

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Two identical particles each of mass $m$ are separated by a distance $d$. The axis of rotation passes through the midpoint of $d$ and is perpendicular to the length $d$. If $K$ is the rotational kinetic energy of the system,then the angular frequency $\omega$ is:

MHT CET 2021 All MHT CET

A
$2d \sqrt{\frac{m}{K}}$
B
$\frac{d}{2} \sqrt{\frac{K}{m}}$
C
$\frac{2}{d} \sqrt{\frac{K}{m}}$
D
$\frac{d}{4} \sqrt{\frac{m}{K}}$

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Two identical particles each of mass $m$ are separated by a distance $d$. The axis of rotation passes through the midpoint of $d$ and is perpendicular to the length $d$. If $K$ is the rotational kinetic energy of the system,then the angular frequency $\omega$ is:

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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 $.....$ .

If a body completes one revolution in $\pi \ s$,then the moment of inertia is related to the rotational kinetic energy $(K)$ by which of the following expressions?

$A$ flywheel rotating about a fixed axis has a kinetic energy of $500 \text{ J}$. If its angular frequency is $5 \text{ Hz}$, calculate the moment of inertia of the wheel about the axis of rotation. (Take $\pi^2 = 10$) (in $\text{ kg m}^2$)

Two bodies $A$ and $B$ are rotating freely with moments of inertia $I_A$ and $I_B$ respectively. Given $I_A > I_B$ and their angular momenta are equal. If $K_A$ and $K_B$ are their rotational kinetic energies,then:

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