Comprehension
In the figure shown a uniform conducting rod of mass \( m \) and length \( l \) is suspended in vertical plane by two conducting springs of spring constant \( k \). Upper end of spring are connected to each other by capacitor of capacitance \( C \). A uniform horizontal magnetic field \( \left(B_{0}\right) \) perpendicular to plane of spring exists in space. Initially rod is in equilibrium but if centre of rod is pulled down and released, it performs SHM. Assume that the spring is small and neglect the magnetic force of interaction between circular section of springs and self inductance of rod.
Find time period of oscillation of rod
(a) \( 2 \pi \sqrt{\frac{m}{k}} \)
(b) \( 2 \pi \sqrt{\frac{B^{2} l^{2} C}{k}} \)
(c) \( \pi \sqrt{\frac{m+B^{2} l^{2} C}{k}} \)
(d) \( 2 \pi \sqrt{\frac{B^{2} l^{2} C+m}{2 k}} \)
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