A vessel filled with water is kept on a weighing pan and the scale adjusted to zero. A block of mass $\mathrm{M}$ and density $\rho $ is suspended by a massless spring of spring constant $\mathrm{k}$. This block is submerged inside into the water in the vessel. What is the reading of the scale ?
A vessel filled with water is kept on a weighing pan and the scale adjusted to zero. A block of mass $\mathrm{M}$ and density $\rho $ is suspended by a massless spring of spring constant $\mathrm{k}$. This block is submerged inside into the water in the vessel. What is the reading of the scale ?
Take a figure into consideration.
The scale is adjusted to zero. Therefore, when a block suspended to a spring is immersed in water, then the reading of the scale will be equal to the upthrust on the block due to water. Upthrust experienced by the block = weight of displaced water
$=(\mathrm{V}) \rho_{\mathrm{w}} \mathrm{g}(\mathrm{V}=$ volume of block $)$
$=\frac{m}{\rho} \rho_{w} g \quad\left(\rho_{w}=\right.$ density of water $)$
$=\left(\frac{\rho_{\mathrm{w}}}{\rho}\right) m g(\rho=$ density of block $)$
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