A sphere is rolling without slipping with velocity $V_0$ on a thin plank moving with $3V_0$ as show in figure. Find distance of instantaneous axis of rotation from centre of sphere.

A disc in rolling without slipping on smooth horizontal surface such that velocity of a COM is $V_0$. Find velocity of point shown in the figure using instantaneous axis of rotation.

A rod of mass $m$ and length $l$ is placed on a frictionless horizontal surface. Velocities of its ends are as shown in figure, then total kinetic energy of the rod is

A rod (mass $m$, length $l$) is placed vertically on smooth horizontal surface. Rod is released and after some time velocity of COM of rod became $V_0$ and at this moment rod makes $60°$ with horizontal. Find angular momentum of rod about ICOR.

A uniform solid hemisphere of radius $r$ is joined to a uniform solid right circular cone of base radius $r$. Both have same density. The centre of mass of the composite solid lies on the common face. The height $\left(h\right)$ of the cone is 

Two particles of equal mass are projected simultaneously with speeds $20 \mathrm{m} {\mathrm{s}}^{-1}$ and $10\sqrt{3} \mathrm{m} {\mathrm{s}}^{-1}$ as shown in figure. Find the maximum height reached by the centre of mass of the particles.

A man of mass $50 \mathrm{kg}$ is standing on a $100 \mathrm{kg}$ plank kept on a frictionless horizontal floor. Initially both are at rest. If the man starts walking on the plank with speed $6 \mathrm{m} {\mathrm{s}}^{-1}$ towards right relative to the plank, then amount of muscular energy spent by the man is

Two smooth prisms of similar right-triangular sections are arranged on a smooth horizontal plane, as shown in figure. The lower prism has a mass $\eta$ times the upper prism. The prisms are held in an initial position as shown and are then released. As the upper prism touches the horizontal plane, the distance moved by the lower prism is