If the rotational kinetic energy of a body is increased by $300\ \%$,then the percentage increase in its angular momentum 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 ...... $J$.

$A$ molecule consists of two atoms each of mass $m$ and separated by a distance $d$. At room temperature,the average rotational kinetic energy is $E$. What is its angular frequency?

Two rotating bodies $P$ and $Q$ of masses $m$ with moment of inertia $I_P$ and $I_Q$ $(I_Q > I_P)$ have equal kinetic energy of rotation. If $L_P$ and $L_Q$ are their angular momenta respectively,then:

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 $.....$ .

$A$ body is rotating about its own axis. Its rotational kinetic energy is $x$ and its angular momentum is $y$. Hence,its moment of inertia about its own axis is: