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A container accelerates horizontally to the left with acceleration g/2. A uniform rod of length L is partially submerged vertically in a liquid contained in the accelerating container. The density of the liquid is rho and the density of the rod is rho/2. If the length of the rod submerged in the liquid is sqrt(a/b)*L, where a and b are the least positive integers (in lowest terms), find (a + b).
- 3
- 5
- 7
- 6
Correct answer: 5
Solution
In the non-inertial frame of the accelerating container, the effective gravitational field tilts but its magnitude doesn't affect the fraction submerged for a vertical rod (the g_eff cancels from both buoyancy and weight). The fraction submerged = (density of rod)/(density of liquid) = (rho/2)/rho = 1/2. So L_sub = (1/2)*L = sqrt(1/4)*L, giving a = 1, b = 4, a + b = 5.
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