Question

In the List-I below, four different paths of a particle are given as functions of time. In these functions,

α

and

β

are positive constants of appropriate dimensions and

α \neq = β

. 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:

p

is the linear momentum,

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
(P)

r (t) = α t \overset{}{^} + β t \overset{}{^}

(Q)

r (t) = α cos ω t \overset{}{^} + β sin ω t \overset{}{^}

(R)

r (t) = α (cos ω t \overset{}{^} + sin ω t \overset{}{^})

(S)

r (t) = α t \overset{}{^} + \frac{β}{2} t^{2} \overset{}{^}

LIST-II
(1)

p

(2)

L

(3)

K

(4)

U

(5)

E

LIST-I
(P) $\vec{r}(t)=\alpha t \hat{\imath}+\beta t \hat{\jmath}$
(Q) $\vec{r}(t)=\alpha \cos \omega t \hat{\imath}+\beta \sin \omega t \hat{\jmath}$
(R) $\vec{r}(t)=\alpha(\cos \omega t \hat{\imath}+\sin \omega t \hat{\jmath})$
(S) $\vec{r}(t)=\alpha t \hat{\imath}+\frac{\beta}{2} t^{2} \hat{\jmath}$

LIST-II
(1) $\vec{p}$
(2) $\vec{L}$
(3) $K$
(4) $U$
(5) $E$

Accepted Answer

(A) $\mathrm{P} \rightarrow 1,2,3,4,5 ; \quad \mathrm{Q} \rightarrow 2,5 ; \quad \mathrm{R} \rightarrow 2,3,4,5 ; \mathrm{S} \rightarrow 5$

Answer

(B) $\mathbf{P} \rightarrow \mathbf{1 , 2 , 3 , 4 , 5 ;} \mathbf{Q} \rightarrow \mathbf{3 , 5} ; \quad \mathbf{R} \rightarrow \mathbf{2 , 3 , 4 , 5} ; \quad \mathrm{S} \rightarrow 2,5$

Answer

(C) $\mathrm{P} \rightarrow 2,3,4 ; \quad \mathrm{Q} \rightarrow 5 ; \quad \mathrm{R} \rightarrow 1,2,4 ; \quad \mathrm{S} \rightarrow 2,5$

Answer

(D) $\mathbf{P} \rightarrow \mathbf{1 , 2 , 3 , 5} ; \quad \mathbf{Q} \rightarrow \mathbf{2 , 5} ; \quad \mathrm{R} \rightarrow \mathbf{2 , 3 , 4 , 5} ; \quad \mathrm{S} \rightarrow 2,5$

JEE Advanced · 2018 · 20 May 2018 · Paper 2 · Rotational Mechanics

Solution

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