The same weight needs more volume

A floating density instrument has mass 30 g and a uniform stem of area 1.5 cm² across both waterlines. It moves from a liquid of density 1000 kg/m³ to one of density 750 kg/m³. Only the stem crosses the surfaces and the instrument remains upright.

How much farther does it sink in the second liquid?

Organize the givens & assumptions

M = 0.030 kg
Stem area = 1.5 × 10⁻⁴ m²
ρ₁ = 1000 kg/m³
ρ₂ = 750 kg/m³

Settled hydrostatic equilibrium in uniform gravity; stable stated orientation, no contact forces unless stated, negligible air buoyancy and surface tension, no absorption, trapped gas or spilling.

A $5.00\ \mathrm{cm}$
B $6.67\ \mathrm{cm}$
C $26.7\ \mathrm{cm}$
D $20.0\ \mathrm{cm}$

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