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List-I describes four systems, each with two particles A and B in relative motion as shown in figures. List-II gives possible magnitudes of their relative velocities (in m s –1 ) at time t = 3 π 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 = 2 π , respectively. (P) 2 1 3 + CAREER POINT Kota H.O. : Career Point Ltd., CP Tower, IPIA, Road No.1, Kota (Raj.), Ph: 080-47250011 www.careerpoint.ac.in 7 Paper-1 (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 = 2 5 π 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) 2 ) 1 – 3 ( (III) Two harmonic oscillators A and B moving in the x direction according to x A = x 0 sin 0 t t and x B = x 0 sin ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ π + 2 t t 0 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 xy 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) 1 25 2 + π Which one of the following options is correct ?

1. I → R, II → T, III → P, IV → S
2. I → S, II → P, III → Q, IV → R
3. I → S, II → T, III → P, IV → R
4. I → T, II → P, III → R, IV → S

Correct answer: I → S, II → T, III → P, IV → R

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