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A metallic ring of mass 2 kg and radius 1 m with a uniform metallic spoke of same mass 2 kg and length 1 m is rotated about its axis with angular velocity 1 rev sec - 1 . In a perpendicular uniform magnetic field B of magnitude 10 T as shown in the figure. If the central end of the spoke is connected to the rim of the wheel through a resistor R of magnitude π Ω as shown. The resistor does not rotate, it's one end is

Options

  1. A10   N
  2. B20   N
  3. C50   N
  4. DNone of these

Correct answer

C. 50   N

Step-by-step solution

F b = B I L Induced current: I = B ω r 2 2 R ∴   F B = B   B ω r 2 2 R r = B 2 ω r 3 2 R To maintain constant angular velocity: F   r = F B r 2 ⇒       F = F B 2 = B 2 ω r 3 4 R = 10 2 × 2 π × 1 3   4 × π = 50   N

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