A particle $\left(5\mathrm{kg}\right)$ moves upon straight line with constant velocity $2 \mathrm{m} {\mathrm{s}}^{-1}$ along the straight line $2y=3x+4$. The angular momentum of particle about origin, in $\mathrm{kg} {\mathrm{m}}^2 {\mathrm{s}}^{-1}$ will be

A rod of mass $m$ and length $2R$ is fixed along the diameter of the ring of same mass $m$ and radius $R$ as shown in figure. The combined body is rolling without slipping along $x$-axis. Then the angular momentum about $z$-axis is having magnitude equal to

A small ball of mass $m$ tied to a string is whirled around in a horizontal circle. The length of the string is gradually decreased by pulling it as shown. If $r$ is the radius of the circular path at any instant, the tension will be proportional to

A thin uniform circular disc of mass $M$ and radius $R$ is rotating in a horizontal plane about an axis passing through its centre and perpendicular to its plane with an angular velocity $\omega$. Another disc of same dimensions but of mass $\frac{1}{4}M$ is placed gently on the first disc coaxially. The angular velocity of the system is

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.