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A cube of edge a floats on a liquid of density rho with a coin of mass m resting on its top. With the coin in place the cube sinks to a depth x1; after the coin is taken off it floats with a smaller depth x2 submerged. Determine (x1 - x2).
- m/(rho*a²)
- rho*a⁴/m
- m/(2*rho*a²)
- data insufficient
Correct answer: m/(rho*a²)
Solution
For floating, buoyancy balances weight. With the coin, rho*g*a²*x1 = (M + m)*g; without it, rho*g*a²*x2 = M*g, where M is the block's mass. Subtracting eliminates M: rho*g*a²*(x1 - x2) = m*g, so x1 - x2 = m/(rho*a²).
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