Question

A ring of mass m and radius 'r' is mounted on a light rod which is suspended by means of two string. Find the tension in the strings if the ring carries a current i and a vertical magnetic field $\beta$ exists. Given
$(\frac{i{a}^{2}B}{l}=\frac{mg}{2\pi })$.

• A. $\frac{mg}{2},\frac{mg}{2}$
• B. $O,mg$
• C. $\frac{mg}{3},\frac{2mg}{3}$
• D. $\frac{3mg}{4},\frac{mg}{4}$

Answer 1

The correct option is D $\frac{3mg}{4},\frac{mg}{4}$


$\frac{i{a}^{2}B}{l}=\frac{mg}{2\pi }$
$\sum F_y=0$
$T_1+T_2-mg=0\Rightarrow T_1+T_2=mg$
$\sum {\tau }_0=0$
$T_{1}l-T_{2}l-MBsin{90}^{\circ }=0$
$\Rightarrow T_1-T_2=\frac{i\pi a^{2}B}{l}$
$T_1-T_2=\frac{mg}{2\pi }\times \pi$
$2T_1=\frac{3mg}{2}$
$\Rightarrow T_1=\frac{3mg}{4},T_2=\frac{mg}{4}$