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Question: Two points of a rod move with velocities 3v and v perpendicular to the rod and in the same direction...

Two points of a rod move with velocities 3v and v perpendicular to the rod and in the same direction, separated by a distance 'r'. Then the angular velocity of the rod is –

A

3vr\frac{3v}{r}

B

4vr\frac{4v}{r}

C

5vr\frac{5v}{r}

D

2vr\frac{2v}{r}

Answer

2vr\frac{2v}{r}

Explanation

Solution

wrod = wpoint = [Vrel.r]\left\lbrack \frac{V_{rel.}}{r} \right\rbrack ; Vrel being the velocity of one point w.r.t other = 3v−vr\frac{3v - v}{r} and 'r' being the distance between them = 2vr\frac{2v}{r}