$A$ person standing on a rotating table holds weights in their outstretched hands and is rotating. They suddenly pull their hands in close to their body. Which statement is true?

$A$ metre stick is pivoted about its centre. $A$ piece of wax of mass $20 \,g$ travelling horizontally and perpendicular to it at $5 \,m/s$ strikes and adheres to one end of the stick so that the stick starts to rotate in a horizontal circle. Given the moment of inertia of the stick and wax about the pivot is $0.02 \,kg \cdot m^2$,the initial angular velocity of the stick is ........... $rad/s$.

If the radius of the Earth becomes $1/n^{th}$ of its present value,without any change in its mass,then the duration of the day becomes:

$A$ small disk is attached to the end of a light inextensible string,which passes through a hole in a frictionless horizontal tabletop. Initially,the disk moves on a circle of radius $R$ with kinetic energy $K_0$. The string is then slowly pulled so that the disk finally rotates on a circle of radius $\frac{R}{\eta}$. What is the work $W$ done in pulling the string?

$A$ 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

$A$ disc of mass $M$ and radius $R$ is rolling with angular speed $\omega$ on a horizontal plane as shown. The magnitude of angular momentum of the disc about the origin $O$ is