A roller is made by joining together two cones at their vertices O. It is kept on two rails AB and CD which are placed asymmetrically (see figure), with its axis perpendicular to CD and its centre O at the centre of line joining AB and CD (see figure). It is given a light push so that it starts rolling with its centre O moving parallel to CD in the direction shown. As it moves, the roller will tend to:

In the figure shown $ABC$ is a uniform wire. If the center of mass of the wire lies vertically below point $A$, then $\frac{BC}{AB}$ is close to

A particle of mass $2 \mathrm{kg}$ is on a smooth horizontal table and moves in a circular path of radius $0.6 \mathrm{m}$. The height of the table from the ground is $0.8 \mathrm{m}$. If the angular speed of the particle is $12\mathrm{ }\mathrm{rad}\mathrm{ }{\mathrm{s}}^{-1}$ , the magnitude of its angular momentum about a point on the ground right under the center of the circle is: