In the Column-I below

PHYSICS · Single correct · AP · Physics 1: Algebra-based · Energy and Momentum of Rotating Systems · Energy and Momentum of Rotating Systems

Problem

In the Column-I below, four different paths of a particle are given as functions of time. In these functions, α\alpha and β\beta are positive constants of appropriate dimensions and α≠β\alpha \neq \beta . In each case, the force acting on the particle is either zero or conservative. In Column-II, five physical quantities of the particle are mentioned p⃗\vec{p} is the linear momentum, L⃗\vec{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. [Adv. 2018]
Column-IColumn-II
P. r⃗(t)=αti^+βtj^\vec{r}(t) = \alpha t \hat{i} + \beta t \hat{j}1. p⃗\vec{p}
Q. r⃗(t)=αcos⁡ωti^+βsin⁡ωtj^\vec{r}(t) = \alpha \cos \omega t \hat{i} + \beta \sin \omega t \hat{j}2. L⃗\vec{L}
R. r⃗(t)=α(cos⁡ωti^+sin⁡ωtj^)\vec{r}(t) = \alpha(\cos \omega t \hat{i} + \sin \omega t \hat{j})3. K
S. r⃗(t)=αti^+β2t2j^\vec{r}(t) = \alpha t \hat{i} + \frac{\beta}{2} t^2 \hat{j}4. U
5. E
(1) P →\to 1, 2, 3, 4, 5; Q →\to 2, 5; R →\to 2, 3, 4, 5; S →\to 5 (2) P →\to 1, 2, 3, 4, 5; Q →\to 3, 5; R →\to 2, 3, 4, 5; S →\to 2, 5 (3) P →\to 2, 3, 4; Q →\to 5; R →\to 1, 2, 4; S →\to 2, 5 (4) P →\to 1, 2, 3, 5; Q →\to 2, 5; R →\to 2, 3, 4, 5; S →\to 2, 5

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