Two particles `A` and `B` are situated at a distance `d = 2m` apart. Particle `A` has a velocity of `10 m//s` at an angle of `60^@` and particle `B` has a velocity `v` at an angle `30^@` as shown in figure. The distance `d` between `A` and `B` is constant. the angular velocity of `B` with respect to `A` is :
.

Options

A. `5 sqrt(3) rad//s`
B. `(5)/(sqrt(3)) rad//s`
C. `10 sqrt(3) rad//s`
D. `(10)/(sqrt(3)) rad//s`

Answer

B

Explanation

(b) If distance between them remains constant, then `v cos 30^@ = u cos 60^@`
`rArr v (sqrt(3))/(2) = 10 (1)/(2) rArr v = (10)/(sqrt(3))`
`omega = v sin 30^@ - u sin 60^@)//d`
=`((10)/(sqrt(3)) xx (1)/(2) -(10 xx sqrt(3))/(2))/(2) = - "(5)/(sqrt(3))rad//s`.