Rigid Body Motions

Q. A shell is fired from a cannon. At the instant the shell is just 3 m/s, while the barrel is swimming upwards with a constant angular velocity of 2 rad/s. The magnitude of the absolute velocity of the shell is

1. $3\frac{m}{s}$
2. $4\frac{m}{s}$
3. $5\frac{m}{s}$
4. $7\frac{m}{s}$

Q. A and B are the endpoints of a diameter of a disc rolling along a straight line with a counterclockwise angular velocity as shown in figure. Referring to the velocity vectors ${\overrightarrow{V}}_{A}and{\overrightarrow{V}}_B$ shown in the figure

1. ${\overrightarrow{V}}_{A}and{\overrightarrow{V}}_B$ are both correct
2. ${\overrightarrow{V}}_A$ is incorrect but ${\overrightarrow{V}}_B$ is correct
3. ${\overrightarrow{V}}_{A}and{\overrightarrow{V}}_B$ are both incorrect
4. ${\overrightarrow{V}}_A$ is correct but ${\overrightarrow{V}}_B$ is incorrect

Q. 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

1. $1\frac{m}{s}$
2. $\sqrt{2}\frac{m}{s}$
3. $\sqrt{3}\frac{m}{s}$
4. $2\frac{m}{s}$