$A$ uniform circular disc of mass $1.5 \ kg$ and radius $0.5 \ m$ is initially at rest on a horizontal frictionless surface. Three forces of equal magnitude $F=0.5 \ N$ are applied simultaneously along the three sides of an equilateral triangle $XYZ$ with its vertices on the perimeter of the disc (see figure). One second after applying the forces,the angular speed of the disc in $\text{rad } s^{-1}$ is:

$A$ ring of mass $M$ and radius $R$ sliding with a velocity $v_0$ suddenly enters a rough surface where the coefficient of friction is $\mu$,as shown in the figure. Choose the correct statement$(s)$.

$A$ projectile of mass $3m$ explodes at the highest point of its path. It breaks into three equal parts. One part retraces its path,the second one comes to rest. The distance of the third part from the point of projection when it finally lands on the ground is ........$m.$ (The range of the projectile was $100\,m$ if no explosion would have taken place.)

If the earth suddenly contracts to $(1/3)^{rd}$ of its present size without any change in its mass, the ratio of the kinetic energy of the earth after and before contraction will be (Earth is assumed to be a rotating sphere about itself).

This question has Statement $1$ and Statement $2$. Of the four choices given after the Statements,choose the one that best describes the two Statements.
Statement $1$ : When the moment of inertia $I$ of a body rotating about an axis with angular speed $\omega$ increases,its angular momentum $L$ remains unchanged,but the kinetic energy $K$ decreases if no external torque is applied.
Statement $2$ : $L = I\omega$ and the rotational kinetic energy $K = \frac{1}{2}I\omega^2 = \frac{L^2}{2I}$.

$A$ uniform disc is rolling on a horizontal surface. At a certain instant,$B$ is the point of contact and $A$ is the topmost point of the disc,where $R$ is the radius of the disc.