Two sphere each of mass $\mathrm{M}$ and radius $\frac{\mathrm{R}}{2}$ are connected with a massless rod of length $2\mathrm{R}$ as shown in the figure. What will be the moment of inertia of the system about an axis passing through the centre of one of the spheres and perpendicular to the rod :

A solid sphere is placed on a horizontal plane. A horizontal impulse $I$ is applied at a distance $h$ above the central line as shown in the figure. Soon after giving the impulse, the sphere starts rolling. The ratio $\frac{h}{R}$ would be,

A ring of radius $3a$ is fixed rigidly on a table. A small ring whose mass is $m$ and radius $a$ rolls without slipping inside it as shown in the figure. The small ring is released from position $A$. When it reaches the lowest point, the speed of the centre of the ring at that time would be,

The moment of inertia of semicircular plate of radius $R$ and mass $M$ about axis $AA\mathit{\text{'}}$ in its plane passing through its centre is

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

A man can move on a horizontal plank supported symmetrically as shown. The variation of normal reaction on support A with distance $x$ of the man from the end of the plank is best represented by

Find minimum height of obstacle so that the sphere can stay in equilibrium

A disc of radius $R$ is rolling purely on a flat horizontal surface, with a constant angular velocity. The angle between the velocity and acceleration vectors of point $P$ is