Question

A simple pendulum is oscillating in a region of uniform magnetic field as shown. As it travels from position $\text{P}$, towards mean position,

• A. Tension in the string increases
• B. Tension in the string decreases
• C. Speed of pendulum decreases
• D. Both $\left(A\right)$ and $\left(C\right)$ are correct.

Answer 1

The correct option is A Tension in the string increases

As we know that, magnetic force on moving charged body in a mgnetic field is given by

${\overrightarrow{F}}_m=q(\overrightarrow{v}\times \overrightarrow{B})$

$F_m=qvB(\because v\perp B)$


So, from given FBD,

$T=mg\cos \theta +F_m$

$T=mg\cos \theta +Bqv$

As the pendulum moves towards mean position, $v$ increases so that $F_m$ increases. Also, as $\theta$ decreases, $\cos \theta$ increases so that $mg\cos \theta$ increases.

Due to these two reasons, tension in the string increases.

Therefore, option $\left(a\right)$ is correct.