Question

A rod of mass $\text{m}$ and length $2 \text{l}$ is connected to two massless strings as shown in figure. A wooden disc of the same mass $\text{m}$ is fixed at the mid-point of the rod in such a way that the plane of the disc is perpendicular to the rod. A massless wire is wrapped around the disc and it is carrying a current $I$ . There is vertically upward magnetic field $\text{B}$ at the location of disk. (Sense of current in the loop when seen from string P side is clockwise)





The tension in the string $\text{P}$ is

• A. $mg+\frac{I \pi R^{2} B}{2 l}$
• B. $mg-\frac{I \pi R^{2} B}{2 l}$
• C. $mg$
• D. $2mg$

Answer 1

Answer: (A)

net torque about the disc is zero
$T_{P}\times l=T_{Q}\times l+I\pi R^{2}B$
and $T_{P}+T_{Q}=2mg$
Using the above equations we get
$T_{P}=mg+\frac{I\pi R^{2} B}{2 l}$