A body of volume 500 cm³ is suspended from an external support and is fully immersed in water contained in a vessel placed on a weighing machine. The body does not touch the vessel. The weighing-machine reading increases by an amount equivalent to N grams. Find N.
Physics · Fluid Mechanics · pascal law and buoyant force
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Question

A body of volume 500 cm³ is suspended from an external support and is fully immersed in water contained in a vessel placed on a weighing machine. The body does not touch the vessel. The weighing-machine reading increases by an amount equivalent to N grams. Find N.

Physics · Fluid Mechanics · pascal law and buoyant force

G1 Physics · Accepted Answer

The buoyant force on the body is B = ρ(water)Vg. By Newton's third law, the body exerts an equal downward force B on the water. Therefore the weighing machine receives an additional downward force equal to the buoyant force. The equivalent added mass is m(eq) = B/g = ρ(water)V. Using water density 1 g/cm³, m(eq) = 1×500 = 500 g. Hence, N = 500.