On reaching by pure rolling at the bottom of incline the fraction of $\mathrm{KE}$ in rotational motion is $\frac{2}{5}$. Then the objects is perhaps

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