Question

Comprehension:

A conducting rod of mass $m$ and length $l$ is released from rest on a smooth metallic rails placed in vertical plane in a uniform horizontal magnetic field $\left(B\right)$ as shown in the figure. When rod falls, it would cut magnetic field lines and motional emf will be induced. Velocity and acceleration of rod will change with time and after a long time rod will achieve a maximum velocity named as terminal velocity.


Answer the following question based on above discussion.

$\left(v\right)$ Thermal power in the resistor is plotted on $y$-axis, against speed on the $x$-axis, the graph will be a-

• A. Straight line
• B. Parabola
• C. Exponential curve
• D. None of the above

Answer 1

The correct option is B Parabola

The induced emf in the rod, $E=Bvl$

The induced currant through the resistor is,

$i=\frac{Bvl}{R}$

Thermal power, $P=i^{2}R=\left(\frac{B^2{v}^2{l}^2}{R^2}\right)R$

$\Rightarrow P=\frac{B^2{v}^2{l}^2}{R}$


<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, $\left(B\right)$ is the correct answer.