$A$ smooth tube of certain mass closed at both ends is rotated in a gravity-free space and released. The two balls shown in the figure move towards the ends of the tube and stay there. Which statement is incorrect about this whole system?

Different minerals are being mined from within the earth and multi-storeyed complexes are being constructed. Due to this activity,theoretically:

If the earth were to suddenly contract to $\frac{1}{n}^{th}$ of its present radius without any change in its mass,the duration of the new day will be nearly:

$A$ circular disc of mass $M$ and radius $R$ is rotating about its axis with angular speed $\omega_{1}$. If another stationary disc having radius $\frac{R}{2}$ and same mass $M$ is dropped co-axially onto the rotating disc,gradually both discs attain a constant angular speed $\omega_{2}$. The energy lost in the process is $p \%$ of the initial energy. The value of $p$ is:

$A$ solid cube of wood of side $2a$ and mass $M$ is resting on a horizontal surface as shown in the figure. The cube is free to rotate about a fixed axis $AB$. $A$ bullet of mass $m$ $(m << M)$ and speed $v$ is shot horizontally at the face opposite to $ABCD$ at a height of $4a/3$ from the surface to impart the cube an angular speed $\omega$. It strikes the face and embeds in the cube. Then,$\omega$ is close to (Note: The moment of inertia of the cube about an axis perpendicular to the face and passing through the centre of mass is $2Ma^2/3$).

$A$ 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 the same thickness and radius but of mass $\frac{1}{8} M$ is placed gently on the first disc coaxially. The angular velocity of the system is now