Two points `A` and `B` on a disc have velocities `v_1` and `v_2`, respectively, at some moment. Their directions make angles `60^@` and `30^@` respectively, with the line of separation as shown in figure. The angular velocity of disc is :
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Options

A. `(sqrt(3) v_1)/(d)`
B. `(v_2)/(sqrt(3) d)`
C. `(v_2 - v_1)/(d)`
D. `(v_2)/(d)`

Answer

D

Explanation

(d) For rigid body, separation between two points remains same. lt brgt `v_1 cos 60^@ = v_2 cos 30^@`
`(v_1)/(2)=(sqrt(3) v_2)/(2) rArr v_1 = sqrt(3) v_2`
`omega_(disc)|(v_2 sin 30^@ - v_1 sin 60^@)/(d)| = |((v_2)/(2)-(sqrt(3) v_1)/(2))/(d)|`
=`|(v_2 - sqrt(3) xx sqrt(3) v_2)/(2 d)|= (2 v_2)/(2d) = (v_2)/(2) rArromega_(disc) = (v_2)/(d)`.
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