$A$ 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 dimension but of mass $M/4$ is placed gently on the first disc coaxially. The angular velocity of the system now is

$A$ horizontal disc of moment of inertia $4.25 \,kg \cdot m^2$ with respect to its axis of symmetry is spinning counter-clockwise at $15 \,rps$ about its axis,as viewed from above. $A$ second disc of moment of inertia $1.80 \,kg \cdot m^2$ with respect to its axis of symmetry is spinning clockwise at $25 \,rps$ as viewed from above about the same axis and is dropped on top of the first disc. The two discs stick together and rotate as one about their axis of symmetry. The new angular velocity of the system as viewed from above is close to

$A$ thin circular ring of mass $m$ and radius $R$ is rotating about its axis with a constant angular velocity $\omega$. Two objects each of mass $M$ are attached gently to the opposite ends of a diameter of the ring. The ring now rotates with an angular velocity $\omega '$ equal to:

$A$ thin circular ring of mass $M$ and radius $r$ is rotating about its axis with an angular speed $\omega$. Two particles each of mass $m$ are now attached at diametrically opposite points. The angular speed of the ring will become

$A$ thin circular ring of mass $M$ and radius $r$ is rotating with a constant angular velocity $\omega$. Two particles,each of mass $m$,are attached to the opposite ends of a diameter of the ring. The new angular velocity of the ring will be:

$A$ stick of length $L$ and mass $M$ lies on a frictionless horizontal surface on which it is free to move in any way. $A$ ball of mass $m$ moving with speed $v$ collides elastically with the stick at its end as shown in the figure. If after the collision the ball comes to rest,then what should be the mass of the ball?