Given: Inductance, \( L = 2 \, \text{H} \); Capacitance, \( C = 4 \, \mu\text{F} = 4 \times 10^{-6} \, \text{F} \).
Step 1: Formula for Frequency of Oscillation The frequency \( f \) of oscillation for an LC circuit is determined by the formula: \[ f = \frac{1}{2\pi \sqrt{LC}} \] where \( L \) is inductance and \( C \) is capacitance.
Step 2: Substitute the given values The formula is applied with the provided values: \[ f = \frac{1}{2\pi \sqrt{(2 \, \text{H})(4 \times 10^{-6} \, \text{F})}} \] \[ f = \frac{1}{2\pi \sqrt{8 \times 10^{-6}}} \] \[ f = \frac{1}{2\pi \times 2.828 \times 10^{-3}} \] \[ f \approx \frac{1}{1.777 \times 10^{-2}} \] \[ f \approx 56.3 \, \text{Hz} \]
Step 3: Conclusion The calculated frequency of oscillation is approximately \( 50 \, \text{Hz} \) when rounded to the nearest available option.
Answer: Option (b): 50 Hz is the correct answer.