Question

In the figure shown, if the velocity of end A is $v_0$, find the velocity of the end $B$ of the rigid rod at the given instant.

• A. $\frac{v_0}{\sqrt{3}}$
• B. $\frac{2v_0}{\sqrt{3}}$
• C. $v_0\sqrt{\frac{2}{3}}$
• D. $\frac{v_0}{\sqrt{2}}$

Answer 1

The correct option is C $v_0\sqrt{\frac{2}{3}}$

The given situation can be depicted as shown

Due to rigidity constraint, the components of the velocities of the points $A$ and $B$ along the rod should be same.
So, $V_B\cos {30}^{\circ }=V_A\cos {45}^{\circ }$
$⟹V_B=\frac{V_A\cos {45}^{\circ }}{\cos {30}^{\circ }}\Rightarrow V_B=V_0\sqrt{\frac{2}{3}}$