A 2.0 m long metallic rod is rotated with an angular frequency of 100 rad/s about an axis normal to the rod and passing through its one end. A uniform magnetic field of 2.0 T exits parallel to the axis. The emf induced between the two ends of the rod is:

Correct option is A

​$$\begin{aligned}&\textbf{Given:} \\&\text{Length of the rod, } l = 2\, \text{m} \\&\text{Angular frequency, } \omega = 100\, \text{rad/s} \\&\text{Magnetic field strength, } B = 2\, \text{T} \\&\text{One end of the rod has zero linear velocity, while the other has a linear velocity of } \omega l.\end{aligned}$$​$$\text{The average linear velocity } v \text{ of the rod is:} \\v = \frac{\omega l}{2} = \frac{100 \times 2}{2} = 100\, \text{m/s}$$

$$\text{The induced emf } \mathcal{E} \text{ is given by the formula:} \\\mathcal{E} = Blv \\\mathcal{E} = 2 \times 2 \times 100 = 400\, \text{V}$$​​​