A circular ring $\left(2m,R\right)$ with a small insect of mass $m$ at its periphery, is placed upon smooth horizontal surface as shown in figure. The insect starts moving with velocity $v$ w.r.t. ground along the periphery. The angular velocity of rotation of ring, will be

A uniform road of mass $M$ and length $L$ is hinged at the centre. A particle of mass $m$ and speed $u$ sticks after hitting the end of the rod. Find the angular velocity of the rod just after the collision.

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