Question

A vessel filled with water is kept on a weighing pan and the scale adjusted to zero. A block of mass M and density ρ is suspended by a massless spring of spring constant k. This block is submerged inside the water in the vessel. What is the reading of the scale?

Answer 1

Considering the diagram below. Beaker is placed on weighing pan which is filled with water and then scale is adjusted to zero. When block is submerged into water the buoyant force acts on block by water.

By Newton’s III law, this buoyant force acts as reaction force, so block will apply force downward due to which reading on scale increases

This is equal to buoyant force = Vρ_wg

∴ Reading of Weighing scale = \(\frac{M}{ρ}.ρ_\text{w}g\)

\(\frac{ρ_\text{w}}{ρ}.Mg = ρ_\text{w}V_g\)