Question

How could you find the density of an irregular object which floats in the water?

Answer 1

In order to measure the density of an irregular object which floats in water we can use the sinker method in which the term sinker is a weight added to the floating object in order to keep it down and fully immerse it in graduated containers.

Formula used:
$\rho =\dfrac{m}{v}$

Complete step by step solution:
As we consider in the hint, we can use the sinker method to measure the density of an object which floats in the water.

We know that formula for the density is,
$\rho =\dfrac{m}{v}.....\left( 1 \right)$
Where,
$\rho$= density of an object
m = mass of an object.
v = volume of an object.

First measure the mass of an object here we can consider that mass of an object is m.

First pour same water in a container and measure the volume of the water the volume of the water is ${{V}_{W}}$.

Now submerged sinker in water with using thread and measure volume, now new volume is v.

Now tie up sinker with object which has irregular shape and submerged full object with the sinker in the water using thread, the new volume will be ${{V}_{2}}$.

Now if we deduct the volume of the water from ${{v}_{1}}$ we can get volume of the sinker.
Volume of the sinker,
${{V}_{S}}={{V}_{1}}-{{V}_{W}}....\left( 2 \right)$

Similarly if we deduct the volume of the water from ${{V}_{2}}$ we can get a combined volume of an object which is tied up with the sinker.

Volume of the object tied up with the sinker
${{V}_{OS}}={{V}_{2}}-{{V}_{W}}....\left( 3 \right)$

Now if we deduct the volume of the sinker from the combined volume of the object and sink we can get the total volume of an object which has irregular shape.

Volume of an object from the equation (2) and (3)
$\begin{aligned} & \Rightarrow {{V}_{O}}={{V}_{OS}}-{{V}_{S}} \\\ & \Rightarrow {{V}_{O}}=({{V}_{2}}-{{V}_{W}})-\left( {{V}_{1}}-{{V}_{W}} \right) \\\ & \therefore {{V}_{O}}={{V}_{2}}-{{V}_{1}}...\left( 4 \right) \\\ \end{aligned}$

Now substitute value of the equation (4) in the equation (1)
$B=\dfrac{m}{{{V}_{2}}-{{V}_{1}}}....\left( 5 \right)$

With using the equation 5 new can find the density of an object with an irregular shape.

Note:
As an approach to measure density of an object which floats in the water we used sinker method in which first we pour water in a container and measure its volume and then we submerged sinker in the water and measured its volume then we submerged object with the sinker and measure the combine volume and by deducting volume of the water from both of them we get the actual volume of the sinker and object with the sinker then by deducting the volume of the sinker we eventually gets the volume of an object. And then by using the formula of the density we can find the density of a given object.