In the List-$I$ below, four different paths of a particle are given as functions of time. In these functions, $\alpha$ and $\beta$ are positive constants of appropriate dimensions and $\alpha \neq \beta$. In each case, the force acting on the particle is either zero or conservative. In List-II, five physical quantities of the particle are mentioned: $\overrightarrow{ p }$ is the linear momentum, $\bar{L}$ is the angular momentum about the origin, $K$ is the kinetic energy, $U$ is the potential energy and $E$ is the total energy. Match each path in List-$I$ with those quantities in List-$II$, which are conserved for that path.

List-$I$	List-$II$
$P$ $\dot{r}(t)=\alpha t \hat{t}+\beta t \hat{j}$	$1$ $\overrightarrow{ p }$
$Q$ $\dot{r}(t)=\alpha \cos \omega t \hat{i}+\beta \sin \omega t \hat{j}$	$2$ $\overrightarrow{ L }$
$R$ $\dot{r}(t)=\alpha(\cos \omega t \hat{i}+\sin \omega t \hat{j})$	$3$ $K$
$S$ $\dot{r}(t)=\alpha t \hat{i}+\frac{\beta}{2} t^2 \hat{j}$	$4$ $U$
	$5$ $E$

• A

  $P \rightarrow 1,2,3,4,5 ; \quad Q \rightarrow 2,5 ; \quad R \rightarrow 2,3,4,5 ; \quad S \rightarrow 5$

• B

  $P \rightarrow 1,2,3,4,5 ; \quad Q \rightarrow 3,5 ; \quad R \rightarrow 2,3,4,5 ; \quad S \rightarrow 2,5$

• C

  $P \rightarrow 2,3,4 ; \quad Q \rightarrow 5 ; \quad R \rightarrow 1,2,4 ; \quad S \rightarrow 2,5$

• D

  $P \rightarrow 1,2,3,5 ; \quad Q \rightarrow 2,5 ; \quad R \rightarrow 2,3,4,5 ; \quad S \rightarrow 2,5$