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	\(\frac{\sqrt{3}+1}{2}\)
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 \(x_B=x_0 sin(\frac{t}{t_0}+\frac{\pi}{2})\) respectively, starting from t = 0. Take x0 = 1 m, t0 = 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 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	\(\sqrt{2}\)
		T	\(\sqrt{25\pi^{2}+1}\)

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

The Correct Option is C

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