If $I_1$ is the moment of inertia of a thin rod about an axis perpendicular to its length and passing through its centre of mass and $I_2$ is the moment of inertia of the ring about an axis perpendicular to plane of ring and passing through its centre formed by bending the rod, then

A uniform rod $AB$ of length $7 \mathrm{m}$ is undergoing combined rotational and translational motions such that at some instant of time, velocities of its end point $A$ and centre $C$ are both perpendicular to the rod and opposite in direction, having magnitudes $11 \mathrm{m} {\mathrm{s}}^{-1}$ and $3 \mathrm{m} {\mathrm{s}}^{-1}$, respectively as shown in the figure.

The velocity of centre $C$ and angular velocity of the rod remain constant.

A force $F$ is applied on the top of a cube as shown in the figure. The coefficient of friction between the cube and the ground is $\mu .$ If $F$ is gradually increased, the cube will topple before sliding, if

Two uniform rods of equal length but different masses are rigidly joined to form an $L-$shaped body, which is then pivoted as shown in figure. If in equilibrium the body is in the shown configuration, ratio $\frac{M}{m}$ will be

The figure shows a uniform rod lying along the $x-$axis. The locus of all the points lying on the $x-y$ plane, about which the moment of inertia of the rod is same as that about $O$ is