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A cylindrical rod( length L, radius R and density d) is dipped vertically in to a liquid. the rod is connected by a wire to a balance that measures the force to lift the rod. the contact angle
between rod and liquid is θ. If rod is partially immersed so 0.5L is above the surface of liquid. Find the energy needed to raise the rod by small vertical displacement dz. what is the force required for that displacement??

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