AS Daily A Level Physics question
A 2.0 kg wooden block of volume 4.0×10^−3 m^3 is held fully submerged in fresh water by a light vertical string attached to the tank floor. The string is cut and the block rises, then settles floating partially submerged. Which statement must be true?
Answer
The correct answer is A.
Correct: A — The string’s tension was downward and about 20 N; once it floats freely, roughly 50% of the block’s volume is submerged. Fully submerged, the upthrust is ρwater g V ≈ 1000×9.81×0.004 ≈ 39 N, while the weight is mg ≈ 19.6 N, so the string must pull downward with about 39−19.6 ≈ 20 N to hold it; when floating, the submerged fraction equals the density ratio m/(ρwater V) = 2/(1000×0.004) = 0.50. B is wrong because the string must act downward (the fluid pushes up more than weight when fully submerged), not upward, even though the 50% fraction is correct. C is wrong because upthrust equals weight only at floating equilibrium, not when forced fully submerged here; the block will not remain fully submerged once released. D is wrong because 40 N confuses the upthrust with the required tension (which is the difference upthrust−weight), and a less-dense-than-water block cannot end up nearly fully submerged when floating.