$A$ flywheel is used with an engine because it

The position of an object having mass $0.1 \text{ kg}$ as a function of time $t$ is given as $\vec{r} = (10t^2\hat{i} + 5t^3\hat{j}) \text{ m}$. At $t = 1 \text{ s}$, which of the following statements are correct?
$A$. The linear momentum $\vec{p} = (2\hat{i} + 1.5\hat{j}) \text{ kg} \cdot \text{m/s}$.
$B$. The force acting on the object $\vec{F} = (2\hat{i} + 3\hat{j}) \text{ N}$.
$C$. The angular momentum of the object about its origin $\vec{L} = 15\hat{k} \text{ J} \cdot \text{s}$.
$D$. The torque acting on the object about its origin $\vec{\tau} = 20\hat{k} \text{ N} \cdot \text{m}$.
Choose the correct answer from the options given below:

Two point-like objects of masses $20 \text{ g}$ and $30 \text{ g}$ are fixed at the two ends of a rigid massless rod of length $10 \text{ cm}$. This system is suspended vertically from a rigid ceiling using a thin wire attached to its center of mass,as shown in the figure. The resulting torsional pendulum undergoes small oscillations. The torsional constant of the wire is $1.2 \times 10^{-8} \text{ N m rad}^{-1}$. The angular frequency of the oscillations is $n \times 10^{-3} \text{ rad s}^{-1}$. The value of $n$ is

$A$ thin uniform rod of length $L$ and mass $M$ is swinging freely along a horizontal axis passing through its centre. Its maximum angular speed is $\omega$. Its centre of mass rises to a maximum height of [where $g$ is gravitational acceleration]:

Seven identical circular planar disks,each of mass $M$ and radius $R$,are welded symmetrically as shown. The moment of inertia of the arrangement about the axis normal to the plane and passing through the point $P$ is:

$A$ thin rod of mass $M$ and length $a$ is free to rotate in a horizontal plane about a fixed vertical axis passing through point $O$. $A$ thin circular disc of mass $M$ and radius $a/4$ is pivoted on this rod with its center at a distance $a/4$ from the free end so that it can rotate freely about its vertical axis,as shown in the figure. Assume that both the rod and the disc have uniform density and they remain horizontal during the motion. An outside stationary observer finds the rod rotating with an angular velocity $\Omega$ and the disc rotating about its vertical axis with angular velocity $4\Omega$. The total angular momentum of the system about the point $O$ is $\left(\frac{Ma^2\Omega}{48}\right) n$. The value of $n$ is. . . . .