Mercury is poured into a uniform vertical U-tube and water is poured in it. The level of water is the same in both arms. A piece of wood is dropped into one arm and some water, equal in weight to the piece of wood, is added to the other. Then, consider the statements: (I) The level of mercury will be same in both the arms. (II) The level of water will be same in both the arms.
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Question

Mercury is poured into a uniform vertical U-tube and water is poured in it. The level of water is the same in both arms. A piece of wood is dropped into one arm and some water, equal in weight to the piece of wood, is added to the other. Then, consider the statements: (I) The level of mercury will be same in both the arms. (II) The level of water will be same in both the arms.

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G1 Physics · Accepted Answer

Step 1: Use surface-energy/pressure relations: ΔP = 2T/R for a liquid drop or 4T/R for a soap bubble, capillary rise h = 2T cosθ/(ρgr), and surface energy = TΔA. Step 2: Apply force or energy balance to the stated radii and surface areas. Applying these relations to the given data gives A: Both I and II are true. Final answer: A.