AS Daily A Level Physics question
In a lab, a metal object is hung from a spring balance. In air the balance reads 49 N. When the object is fully submerged in water, the reading falls to 39 N. Take the density of water as 1000 kg m−3 and g = 9.8 N kg−1. Which estimate is closest to the object’s volume?
Answer
The correct answer is C.
Correct: C — 0.0010 m^3. The apparent loss of weight (49 N − 39 N = 10 N) equals the weight of displaced water, so 10 = ρ g V ⇒ V = 10/(1000 × 9.8) ≈ 0.0010 m^3. A is a factor of 10 too small, consistent with misusing g (e.g. taking g ≈ 98) or a misplaced decimal. B ignores g and wrongly uses V = F/ρ, giving an answer about ten times too large. C follows the correct relation between upthrust and displaced water weight. D is a factor of 10 too large, as if using an incorrect water density of 100 kg m^3 or misplacing the decimal when converting mass to volume.