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 $\rho$ 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

Step 1: Draw the free body diagram and find the equilibrium equation.

Let $x$ be the extension in the spring.




As the block is in equilibrium,

$Mg-(kx+{\rho }_{w}Vg)=0$

Where ${\rho }_w$ is the density of water and $V$ is the volume of the block.

Step 2: Find the reading of the scale.

As water applies buoyant force $\left(F_B\right)$ on block.

From Newton's third law same force $\left(F_B\right)$ will be aplied by block on water.


From figure

$N=F_B={\rho }_{w}gV$

So, the reading of scale will

$N={\rho }_{w}Vg$

Final Answer$:{\rho }_{w}Vg$