Ncert Exercises & Solutions

Q. 14 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?

Hint: The pressure difference created is distributed uniformly in all directions.

Step 1: Find the weight of the water displaced.

Consider the diagram.

The scale is adjusted to zero, therefore, when the 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.

Thrust=Weight of water displaced

= V ρ_{w} g

(where V is the volume of the block and

ρ_{w}

is the density of water)

= \frac{m}{ρ} ρ_{w} g = (\frac{ρ_{w}}{ρ}) m g

(∵

The density of the block,

ρ = \frac{m a s s}{v o l u m e} = \frac{m}{V}

)

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