Question

A straight rod length L(t), hinged at one end freely extensible at the other end, rotates through an angle $\theta$(t) about the hinge. At time t, L(t)=1 m, $\dot{L}\left(t\right)=1\frac{m}{s},\theta \left(t\right)=\frac{\pi }{4}rad\text{and}\dot{\theta }\left(t\right)=1\frac{rad}{s}$. The magnitude of the velocity at the other end of the rod is

• A. $1\frac{m}{s}$
• B. $\sqrt{2}\frac{m}{s}$
• C. $\sqrt{3}\frac{m}{s}$
• D. $2\frac{m}{s}$

Answer 1

The correct option is B $\sqrt{2}\frac{m}{s}$


Velocity has two components

$\overrightarrow{v}=\sqrt{(1{)}^2+(1{)}^2}=\sqrt{2}\frac{m}{s}$