Question

A conducting rod of negligible mass and length l = 1.2m is hinged at one end at point A while the other end is attached to a spring of constant $k=50N{m}^{-1}$ . The arrangement is placed in transverse uniform magnetic field B = 2T and a current I = 5A is passed through the rod. The figure shows the situation in equilibrium position when the rod makes an angle ${53}^{\circ }$ with the vertical. Choose the correct statement(s)

• A. The elongation in the spring is 0.1m
• B. The elongation in the spring is 0.5m
• C. The energy stored in the spring in equilibrium is 0.5J
• D. The energy stored in the spring in equilibrium is 1J

Answer 1

The correct option is D The energy stored in the spring in equilibrium is 1J

In equilibrium
$ilB\times \frac{1}{2}=kxcos53\times l\Rightarrow x=0.2m$
Energy stored $=\frac{1}{2}k{x}^2$