Physics-
General
Easy

Question

A metallic ring of mass m and radius r with a uniform metallic spoke of same mass m and length r is rotated about its axis with angular velocity omega in a perpendicular uniform magnetic field B as shown. If the central end of the spoke is connected to the rim of the wheel through a resistor R as shown. The resistor does not rotate, its one end is always at the center of the ring and other end is always in contact with the ring. A force F as shown is needed to maintain constant angular velocity of the wheel. F is equal to (The ring and the spoke has zero resistance)

  1. fraction numerator B to the power of 2 end exponent omega r to the power of 2 end exponent over denominator 8 R end fraction    
  2. fraction numerator B to the power of 2 end exponent omega r to the power of 2 end exponent over denominator 2 R end fraction    
  3. fraction numerator B to the power of 2 end exponent omega r to the power of 3 end exponent over denominator 2 R end fraction    
  4. fraction numerator B to the power of 2 end exponent omega r to the power of 3 end exponent over denominator 4 R end fraction    

The correct answer is: fraction numerator B to the power of 2 end exponent omega r to the power of 3 end exponent over denominator 4 R end fraction

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