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.

$\left(iii\right)$ The velocity of the rod when it has achieved its terminal value.

• A. $\frac{mgR}{Bl}$
• B. $\frac{mgR}{B{l}^2}$
• C. $\frac{mgR}{B^2{l}^2}$
• D. $\frac{mgR}{2B^2{l}^2}$

Answer 1

The correct option is C $\frac{mgR}{B^2{l}^2}$

At terminal velocity $\left(v_t\right)$, acceleration of the rod ceases i.e.,$a_{rod}=0$



$\Rightarrow mg=F_m$

$\Rightarrow mg=ilB[\because i=\frac{Bl{v}_t}{R}]$

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

$\Rightarrow v_t=\frac{mgR}{B^2{l}^2}$

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