Question

List I describe four systems, each with two particles, A and B, in relative motion, as shown in the figures. List II gives the possible magnitude 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 ω = 1 rad s–1. The initial angular positions of A and B at time t = 0 are θ = 0 and θ = $\frac{\pi}{2}$, respectively.
	P
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 ).
III	Two harmonic oscillators A and B moving in the x direction according to $x_A = x_0 sin\frac{t}{t_0}$ and $x_B=x_0 sin(\frac{t}{t_0}+\frac{\pi}{2})$ respectively, starting from t = 0. Take x0 = 1 m, t0 = 1 s.
IV	Particle A is rotating in a horizontal circular path of radius 1 m on the xy plane, with constant angular speed ω = 1 rad s–1. Particle B is moving up at a constant speed 3 ms–1 in the vertical direction as shown in the figure. (Ignore gravity)
	S
	T

Which one of the following options is correct?

• A. I → R, II → T, III → P, IV → S
• B. I → S, II → P, III → Q, IV → R
• C. I → S, II → T, III → P, IV → R
• D. I → T, II → P, III → R, IV → S

Answer 1

Answer: (C)

I → S, II → T, III → P, IV → R

Answer 2

The correct answer is option (C): I → S, II → T, III → P, IV → R