Question

List I describes four systems, each with two particles $A$ and $B$ in relative motion as shown in figure. List II gives possible magnitudes of their relative velocities (in $m s^{-1}$) at time $t=\frac{\pi}{3} s$.

| List-I | | List-II | |
| --- | --- | --- | --- |
| (I) | $A$ and $B$ are moving on a horizontal circle of radius $1 m$ with uniform angular speed $\omega=1 rad s^{-1}$. The initial angular positions of $A$ and $B$ at time $t=0$ are $\theta=0$ and $\theta=\frac{\pi}{2}$ respectively.  | (P) | $\frac{\sqrt{3}+1}{2}$ |
| (II) | Projectiles $A$ and $B$ are fired (in the same vertical plane) at $t=0$ and $t=0.1 s$ respectively, with the same speed $v=\frac{5 \pi}{\sqrt{2}} m s^{-1}$ and at 45° from the horizontal plane. The initial separation between $A$ and $B$ is large enough so that they do not collide. $(g=10 m s^{-2})$.  | (Q) | $\frac{(\sqrt{3}-1)}{\sqrt{2}}$ |
| (III) | Two harmonic oscillators $A$ and $B$ moving in the $x$ direction according to $x_{A}=x_{0} \sin \frac{t}{t_{0}}$ and $x_{B}=x_{0} \sin \left(\frac{t}{t_{0}}+\frac{\pi}{2}\right)$ respectively, starting from $t=0$. Take $x_{0}=1 m, t_{0}=1 s$.  | (R) | $\sqrt{10}$ |
| (IV) | Particle $A$ is rotating in a horizontal circular path of radius $1 m$ on the $xy$ plane, with constant angular speed $\omega=1 rad s^{-1}$. Particle $B$ is moving up at a constant speed $3 m s^{-1}$ in the vertical direction as shown in the figure. (Ignore gravity.)  | (S) | $\sqrt{2}$ |
| | | (T) | $\sqrt{25 \pi^{2}+1}$ |

Which one of the following options is correct?

Accepted Answer

(C) I→S, II→T, III→P, IV→R

Answer

(A) I→R, II→T, III→P, IV→S

Answer

(B) I→S, II→P, III→Q, IV→R

Answer

(D) I→T, II→P, III→R, IV→S

JEE Advanced · 2022 · 28 Aug 2022 · Paper 1 · Kinematics

Solution

More JEE Advanced questions on Kinematics

List-I		List-II
(I)	$A$ and $B$ are moving on a horizontal circle of radius $1 m$ with uniform angular speed $ω = 1 r a d s^{- 1}$ . The initial angular positions of $A$ and $B$ at time $t = 0$ are $θ = 0$ and $θ = \frac{π}{2}$ respectively.	(P)	$\frac{3 + 1}{2}$
(II)	Projectiles $A$ and $B$ are fired (in the same vertical plane) at $t = 0$ and $t = 0.1 s$ respectively, with the same speed $v = \frac{5 π}{2} m s^{- 1}$ and at 45° from the horizontal plane. The initial separation between $A$ and $B$ is large enough so that they do not collide. $(g = 10 m s^{- 2})$ .	(Q)	$\frac{( 3 - 1 )}{2}$
(III)	Two harmonic oscillators $A$ and $B$ moving in the $x$ direction according to $x_{A} = x_{0} sin \frac{t}{t _{0}}$ and $x_{B} = x_{0} sin (\frac{t}{t _{0}} + \frac{π}{2})$ respectively, starting from $t = 0$ . Take $x_{0} = 1 m, t_{0} = 1 s$ .	(R)	$10$
(IV)	Particle $A$ is rotating in a horizontal circular path of radius $1 m$ on the $x y$ plane, with constant angular speed $ω = 1 r a d s^{- 1}$ . Particle $B$ is moving up at a constant speed $3 m s^{- 1}$ in the vertical direction as shown in the figure. (Ignore gravity.)	(S)	$2$
		(T)	$25 π^{2} + 1$