Particle A moves with $4 m / s$ along positive $y -$ axis and particle $B$ in a circle $x^{2} + y^{2} = 4$ (anticlockwise) with constant angular velocity $ω = 2 / r a d s$ . At time $t = 0$ particle is at $(2 m, 0)$ . Then

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magnitude of relative velocity between them at time $t$ is $8 \sin t$

magnitude of relative velocity between them at time $t$ is $8 \sin 2 t$

magnitude of relative velocity between them is maximum at $t = \frac{π}{4} s$

magnitude of relative velocity between them is maximum at $t = \frac{π}{2} s$

answer is B, D.

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Detailed Solution

Speed of particle A , $v_{A} = 4 m / s a n d s p e e d o f p a r t i c l e B, v_{B} = ω R = 4 m / s . A t t i m e t, a n g l e b e t w e e n \vec{v_{A}} a n d \vec{v_{B}} i s ω t . T h e r e f o r e, \vec{v_{A B}} = \vec{v_{A}} - \vec{v_{B}} a n d |\vec{v_{A B}}| = |\vec{v_{A}} - \vec{v_{B}}| = 2 v \sin ω t = 2 \times 4 \sin ω t = 8 \sin ω t$