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

$A$ thin rod of length $L$ and mass $M$ is held vertically with one end on the floor and is allowed to fall. Find the velocity of the other end when it hits the floor,assuming that the end on the floor does not slip.

$A$ circular disc has a mass of $1\ kg$ and radius $40\ cm$. It is rotating about an axis passing through its centre and perpendicular to its plane with a speed of $10\ rev/s$. The work done in joules in stopping it would be ...... $J$

$A$ uniform rod of mass $M$ and length $L$ is pivoted at one end and is free to rotate in a vertical plane. The rod is released from rest in a horizontal position. What is the angular velocity of the rod when it reaches the vertical position?

$A$ cord of negligible mass is wound around the rim of a wheel supported by spokes with negligible mass. The mass of the wheel is $10 \ kg$ and the radius is $10 \ cm$. It can rotate freely without any friction. Initially,the wheel is at rest. If a steady pull of $20 \ N$ is applied on the cord,the angular velocity (in $rad/s$) of the wheel,after the cord is unwound by $1 \ m$,would be:

$A$ uniform bar of length $6l$ and mass $8m$ lies on a smooth horizontal table. Two point masses $m$ and $2m$ moving in the same horizontal plane with speeds $2v$ and $v$ respectively,strike the bar (as shown in the figure) and stick to the bar after the collision. The total energy after the collision (about the center of mass,$c$) will be: