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 into the water in the vessel. What is the reading of the scale?

Answer 1

As shown in the diagram, A block of mass M and density p is suspended by a massless spring of spring constants k. This block is submerged in the water in the vessel.

The scale is adjusted to zero, therefore, when the block suspended in spring is immersed in water, then the reading of the scale will be equal to the upthrust on the block due to water.

As we submerge the block into the water, a force equal to the weight of the block acts upward in the form of a buoyant force. So, the downward force applied by the block equals to VP_wg

V = the water volume which is displaced by the block

P_w = density of water

Mass of block = M = V

${\displaystyle V=\frac{M}{p}}$

So, the reading on the weighing scale reads: ${\displaystyle \frac{M}{p}.p_{w}g=\frac{p_w}{p}Mg}$

Important point: If the scale is not adjusted to zero as said earlier, the reading on the scale will be different. The weight of the vessel and the weight of water is also added to the reading.