Question

The velocity of point $P$ when system rotates by an angle $\frac{\pi }{2}$

• A. $\frac{5J}{66\lambda a}$
• B. $\frac{19J}{66\lambda a}$
• C. $\frac{33J}{66\lambda a}$
• D. None

Answer 1

The correct option is A $\frac{5J}{66\lambda a}$

When rod rotate by $\frac{\pi }{2}$ rotation velocity

$=\overrightarrow{r}\times \overrightarrow{w}$

$=-\frac{J}{11\lambda a}\hat{J}$

Translation velocity $=\frac{J}{6\lambda a}\hat{J}$

So, total velocity

$=\frac{J}{\lambda a}(\frac{1}{6}-\frac{1}{11})\hat{J}$

$=\frac{5}{66\lambda a}\hat{J}$