In the List-I below, four different paths of a particle are given as functions of time. In these functions, $α a n d β$ 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. Certain statements are given about speed and angular velocity of the particle about origin. Match each path in List-I with those quantities in List-II.
List-I
List-II
(P)
$\vec{r} (t) = α t \hat{i} + β t j$
(1)
Speed is constant
(Q)
$\vec{r} (t) = α (\cos ω t \hat{i} + \sin ω t j)$
(2)
Speed is decreasing with time
(R)
$\vec{r} (t) = α \hat{i} + β t j$
(3)
Speed is increasing with time
(S)
$\vec{r} (t) = α t \hat{i} + \frac{β}{2} t^{2} j$
(4)
Angular velocity is constant

(5)
Angular velocity is decreasing with time

(6)
Angular velocity is increasing with time

Question

In the List-I below, four different paths of a particle are given as functions of time. In these functions, $α a n d β$ 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. Certain statements are given about speed and angular velocity of the particle about origin. Match each path in List-I with those quantities in List-II.

List-I		List-II
(P)	$\vec{r} (t) = α t \hat{i} + β t j$	(1)	Speed is constant
(Q)	$\vec{r} (t) = α (\cos ω t \hat{i} + \sin ω t j)$	(2)	Speed is decreasing with time
(R)	$\vec{r} (t) = α \hat{i} + β t j$	(3)	Speed is increasing with time
(S)	$\vec{r} (t) = α t \hat{i} + \frac{β}{2} t^{2} j$	(4)	Angular velocity is constant
		(5)	Angular velocity is decreasing with time
		(6)	Angular velocity is increasing with time

Infinity Learn · Accepted Answer

$(P) - (3, 5), (Q) - (2, 5), (R) - (2, 4), (S) - (2, 5)$

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