In a uniform field B = 0.049 T a magnetic needle completes 20 oscillations in 5 s. Its moment of inertia is 9.8 × 10⁻⁶ kg·m². If its magnetic moment is x × 10⁻⁵ A·m², find x. [Image]
Options

Question

In a uniform field B = 0.049 T a magnetic needle completes 20 oscillations in 5 s. Its moment of inertia is 9.8 × 10⁻⁶ kg·m². If its magnetic moment is x × 10⁻⁵ A·m², find x. [Image]

G1 Physics · Accepted Answer

Step 1: T = 5/20 = 0.25 s. Step 2: From T = 2π√(I/(mB)), rearrange m = 4π²I/(T²B). Step 3: m = [4π² × 9.8 × 10⁻⁶]/[0.25² × 0.049] = 0.0128π² A·m² = 1280π² × 10⁻⁵ A·m². Step 4: x = 1280π² (option C). Final answer: (C) 1280π².