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A solid block is tied by a string and held fully submerged below the surface of a liquid whose density is greater than that of the solid. When the whole system is at rest, the string tension is T0. If the entire system is then given an upward acceleration a, what is the new tension in the string?

1. T0 (1 + a/g)
2. T0 (1 - a/g)
3. 2 T0 (1 - a/g)
4. 3 T0 (1 + 2a/g)

Correct answer: T0 (1 + a/g)

Solution

At rest, the string (attached to the bottom) holds the block down because buoyant force B exceeds weight W: T0 = B - W = (rho_L - rhoₛ) V g. Under upward acceleration a, effective gravity becomes (g + a), so each force scales by (g+a)/g: T = (rho_L - rhoₛ) V (g + a) = T0 (g + a)/g = T0 (1 + a/g).

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