Question

A rod of length l, negligible resistance and mass m slides on two horizontal frictionless rails of negligible resistance by hanging a block of mass m₁ by the help of insulating mass less string passing through fixed massless pulley, (as shown). If a constant magnetic field B acts upward perpendicular to the plane of the figure, find steady state velocity of hanging mass–

• A. $\frac{m_{1}gR}{B^{2}\mathcal{l}^{2}}$upward
• B. $\frac{m_{1}gR}{B^{2}\mathcal{l}^{2}}$downward
• C. $\frac{mgR}{B^{2}\mathcal{l}^{2}}$upward
• D. $\frac{mgR}{B^{2}\mathcal{l}^{2}}$downward

Answer 1

Answer: (B)

$\frac{m_{1}gR}{B^{2}\mathcal{l}^{2}}$downward

Answer 2

m₁g = T, T = ilB

e = Blv

i =$\frac{B\mathcal{l}v}{R}$

v = $\frac{m_{1}gR}{B^{2}\mathcal{l}^{2}}$downward.