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 then relative velocities (in {m s}^{-1} ) at time t=π/3{ s}. List-I List-II (I) A and B are moving on a horizontal circle of radius 1{ m} with uniform angular speed ω=1{ rad s}^{-1}. The initial angular positions of A and B at time t=0 are θ=0 and θ=π/2 respectively. (P) {{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={5π}{{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) {{3}-1}{{2}} (III) Two harmonic oscillators A and B moving in the x direction according to x_A=x₀ t/t₀ and x_B=x₀ ≤ft(t/t₀+π/2) respectively, starting from t=0. Take x₀=1{ m},\ t₀=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{ 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) {2} (T) {25π²+1} Which one of the following options is correct? [JEE Adv 2022 P1]

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 then relative velocities (in {m s}^{-1} ) at time t=π/3{ s}.   List-I   List-II (I) A and B are moving on a horizontal circle of radius 1{ m} with uniform angular speed ω=1{ rad s}^{-1}. The initial angular positions of A and B at time t=0 are θ=0 and θ=π/2 respectively. (P) {{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={5π}{{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) {{3}-1}{{2}} (III) Two harmonic oscillators A and B moving in the x direction according to x_A=x₀ t/t₀ and x_B=x₀ ≤ft(t/t₀+π/2) respectively, starting from t=0. Take x₀=1{ m},\ t₀=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{ 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) {2}     (T) {25π²+1} Which one of the following options is correct? [JEE Adv 2022 P1]

Examsnet · Accepted Answer

Correct Answer is : I→S, II→T, III→P, IV→RIarrow S,\ IIarrow T,\ IIIarrow P,\ IVarrow RI→S, II→T, III→P, IV→R

	List-I		List-II
(I)	$A$ and $B$ are moving on a horizontal circle of radius $1\text{ m}$ with uniform angular speed $\omega=1\text{ rad s}^{-1}$ . 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 $t=0.1\text{ s}$ respectively, with the same speed $v=\frac{5\pi}{\sqrt{2}}\text{ m s}^{-1}$ and at $45^{\circ}$ from the horizontal plane. The initial separation between $A$ and $B$ is large enough so that they do not collide, $(g=10\text{ m s}^{-2})$ .	(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 $x_0=1\text{ m},\ t_0=1\text{ s}$ .	(R)	$\sqrt{10}$
(IV)	Particle $A$ is rotating in a horizontal circular path of radius $1\text{ m}$ on the $x y$ plane, with constant angular speed $\omega=1\text{ rad s}^{-1}$ . Particle $B$ is moving up at a constant speed $3\text{ m s}^{-1}$ in the vertical direction as shown in the figure. (Ignore gravity.)	(S)	$\sqrt{2}$
		(T)	$\sqrt{25\pi^2+1}$

JEE Advanced 2022 Paper 1