A metre stick is held vertically with one end on the floor and is then allowed to fall. Assuming that the end of the stick on the floor does not slip, the velocity of the other end when it hits the floor, will be

A uniform bar of length $6$ and mass $8\mathrm{m}$ lies on a smooth horizontal table. Two point masses $\mathrm{m}$ and $2 \mathrm{m}$ moving in the same horizontal with speed $2\mathrm{v}$ and $\mathrm{v}$ respectively, strike the bar as shown in the figure, and stick to the bar after the collision. Denoting angular velocity (about the centre of mass), total energy and centre of mass velocity by $\omega , E$ and $v_{\mathit{c}}$ respectively, we have after the collision:

A sphere is rolling without slipping on a fixed horizontal plane surface. In the figure, $A$ is the point of contact, $B$ is the centre of the sphere and $C$ is the topmost point. Then

A cubical block of side$a$ is moving with a velocity $\mathrm{v}$ on a horizontal smooth plane as shown in the figure. It hits a ridge at the point $O$. The angular speed of the block after it hits the ridge at $O$ is:

A uniform rod $AB$ of mass $\mathrm{m}$ and length $L$ is suspended by two strings $C$ and $D$ of negligible mass as shown in the figure  When the string $D$ is cut, the tension in the string $C$ will be: