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A uniform cylindrical rod of length 2L and specific gravity 0.75 floats partially immersed in water, supported by a string attached to one of its ends (the lower end is tied to the bottom of the container). Which of the following statements is/are correct? (A) The length of rod extending out of water is L. (B) The length of rod extending out of water is L/2. (C) The tension in the string is (1/2)*rho_w*A*L*g. (D) The tension in the string is rho_w*A*L*g.

1. The length of rod that extends out of water is L
2. The length of rod that extends out of water is L/2
3. Tension in the string is 1/2 rho_w A L g
4. Tension in the string is rho_w A L g

Correct answer: The length of rod that extends out of water is L/2

Solution

By torque equilibrium about the fixed string end (lower end), the submerged length works out such that the rod's geometry gives L/2 extending above water. Vertical equilibrium then gives tension T = rho_w*A*L_sub*g - 0.75*rho_w*A*2L*g = (1/2)*rho_w*A*L*g.

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