A uniform bar of length 12 cm and mass 20 m lies on a smooth horizontal table. Two point masses $m$ and $2 m$ are moving in opposite directions with same speed of $v$ and in the same plane as the bar, as shown in figure. These masses strike the bar simultaneously and get stuck to it. After collision the entire system is rotating with angular frequency $\omega$. The ratio of $v$ and $\omega$ is :

A laser beam has intensity of $4.0 \times 10^{14} \mathrm{~W} / \mathrm{m}^2$. The amplitude of magnetic field associated with beam is $\_\_\_\_$ T.

(Take $\epsilon_{\mathrm{o}}=8.85 \times 10^{-12} \mathrm{C}^2 / \mathrm{Nm}^2$ and $\mathrm{c}=3 \times 10^8 \mathrm{~m} / \mathrm{s}$ )

Five positive charges each having charge $q$ are placed at the vertices of a pentagon as shown in the figure. The electric potential $(V)$ and the electric field $(\vec{E})$ at the center $O$ of the pentagon due to these five positive charges are :

Given below are two statements :

Statement I : An object moves from position $r_1$ to position $r_2$ under a conservative force field $\vec{F}$. The work done by the force is $W=-\int\limits_{r_1}^{r_2} \vec{F} \cdot \overrightarrow{d r}$.

Statement II : Any object moving from one location to another location can follow infinite number of paths. Therefore, the amount of work done by the object changes with the path it follows for a conservative force.

In the light of the above statements, choose the correct answer from the options given below :