A particle of mass $m$ moves along line $PC$ with velocity $v$ as shown.What is the angular momentum of the particle about $O$ ?

A thin rod of length $L$ and mass $M$ is bent at its mid-point into two halves so that the angle between them is $90^o$. The moment of inertia of the bent rod about an axis passing through the bending point and perpendicular to the plane defined by the two halves of the rod is

A thin rod of mass $m$ and length $l$ is oscillating about horizontal axis through its one end. Its maximum angular speed is $\omega $. Its centre of mass will rise upto maximum height

We have two spheres, one of which is hollow shell and the other solid. They have identical masses and moment of inertia about their respective diameters. The ratio of their radius is given by

Three particles are connected by massless rods lying along the $y-$ axis. If the system rotates about the $x-$ axis with an angular speed of $2\, rad/s$, the $M.I.$ of the system is ......... $kg-m^2$

Two racing cars of masses $m_1$ and $m_2$ are moving in circles of radii $r_1$ and $r_2$ respectively. Their speeds are such that each makes a complete circle in the same time $t$. The ratio of the angular speeds of the first to the second car is