Questions in rotational-motion

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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 ${{{I}_{2}}}/{{{I}_{1}}=4}\;$ then $\frac{{{r}_{2}}}{{{r}_{1}}}$ equals
The moment of inertia of a sphere (mass M and radius R) about it's diameter is $I$. Four such spheres are arranged as shown in the figure. The moment of inertia of the system about axis $XX'$ will be
Three identical thin rods each of length l and mass M are joined together to form a letter H. What is the moment of inertia of the system about one of the sides of H
Moment of inertia of a sphere of mass M and radius R is I. Keeping $M$ constant if a graph is plotted between I and R, then its form would be
Three particles are situated on a light and rigid rod along $Y$axis as shown in the figure. If the system is rotating with an angular velocity of $2\,rad/\sec $about $X$axis, then the total kinetic energy of the system is
On account of melting of ice at the north pole the moment of inertia of spinning earth
According to the theorem of parallel axes $I={{I}_{g}}+M{{d}^{2}}$, the graph between $I$ and $d$ will be
What is the moment of inertia of a square sheet of side $l$ and mass per unit area $\mu $about an axis passing through the centre and perpendicular to its plane
The adjoining figure shows a disc of mass M and radius R lying in the X-Y plane with its centre on $X-$axis at a distance $a$ from the origin. Then the moment of inertia of the disc about the X-axis is
We have two spheres, one of which is hollow and the other solid. They have identical masses and moment of inertia about their respective diameters. The ratio of their radius is given by

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