Question

A uniform rod 'AB' of length l i spinning with an angular velocity $\omega =2v/l$ rad/s while its centre of mass moves with a velocity v m/s, as shown in figure below. The speed of the end A of the rod is

• A. v m/s
• B. 2v m/s
• C. 1.5v m/s
• D. 2.5v m/s

Answer 1

The correct option is A v m/s



Velocity of end A,

${\overrightarrow{V}}_A={\overrightarrow{V}}_{A.C}+{\overrightarrow{V}}_C$

$V_A=\sqrt{V_{AC}^2+V_C^2+2V_{AC}{V}_{C}cos\theta }$

$\underset{V_{AC}}{\to }=\omega \times \frac{l}{2}=2\times \frac{V}{l}\times \frac{l}{2}=v$

we know, $V_C=v$,

$V_{AC}=vand\theta ={90}^o+{30}^o={120}^o$

Hence, $V_A=\sqrt{v^2+v^2+2\times v\times v\times cos{120}^o}$

$V_A=vm/s$