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A horizontal metallic rod of mass m and length l is supported by two vertical identical springs of spring constant, K each and natural length l 0 . A current i is flowing in the rod in the direction shown. If the rod is in equilibrium then the length of each spring in this state is:

Options

  1. Al 0 + i l B - m g K
  2. Bl 0 + ilB - mg 2 K
  3. Cl 0 + m g - i l B 2 K
  4. Dl 0 + m g - i l B K

Correct answer

B. l 0 + ilB - mg 2 K

Step-by-step solution

The force on the rod due to the magnetic field and gravity is i l B - m g     ( u p w a r d s ) Hence the extension in the springs is i l B - m g 2 k ( N o t e that effective spring constant is 2k) Therefore the length of the spring is l 0 + i l B - m g 2 k

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