Question

A conducting rod $\text{AB}$ of mass $100\text{gm}$ and length $10\text{cm}$ is placed on two rails as shown. The rod carries a current of $20\text{A}$ and there is a uniform magnetic field of $1.5\text{T}$ in the surrounding space. What will be the speed of the rod as it travels through $50\text{cm}$ along the rails, if it starts from rest. Take $\mu =0.5$ between rails and rod and $g=10{\text{m/s}}^2$.

• A. $0.5\text{m/s}$
• B. $2.5\text{m/s}$
• C. $5\text{m/s}$
• D. $25\text{m/s}$

Answer 1

The correct option is C $5\text{m/s}$


Magnetic force on the rod:

$F_m=BIl=1.5\times 20\times 0.1=3\text{N}$

Friction force on the rod:

$f=\mu mg=0.5\times (100\times {10}^{-3})\times 10=0.5\text{N}$

As $F_m>f$, the rod will accelerate.

$\therefore$ equation of motion of the rod will be

$F_m-f=ma$

$\Rightarrow 3-0.5=0.1\times a$

$\therefore a=25{\text{m/s}}^2$

Now using, $v^2=u^2+2as$

$\Rightarrow v^2=0+2\times 25\times 0.5$

$\therefore v=5\text{m/s}$

Hence, option (c) is the correct answer.