Question

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

• A. $\frac{3v}{r}$
• B. $\frac{4v}{r}$
• C. $\frac{5v}{r}$
• D. $\frac{2v}{r}$

Answer 1

Answer: (D)

$\frac{2v}{r}$

Let $w$ be the angular velocity of the rod about point O.

For A: $3v=(r+x)w$

For B; $v=xw$

On Subtracting we get, $3v-v=(r+x)w-xw$

$⟹2v=rw$