Question

The volume of a plastic covered sealed box is $350c{{m}^{3}}$ and the box has a mass of 500g. Will the box float on water or sink in water? What will be the mass of water displaced by the box?

Answer 1

As a very first step, one could read the question well and hence note down the given values from the question. Then one could simply recall the expression for density and then substitute the values to get the answer. For the second question, simply apply Archimedes' principle.

Formula used:
Density,
$\rho =\dfrac{M}{V}$

Complete step-by-step solution:
In the question, we are given the volume of a plastic covered sealed box to be $350c{{m}^{3}}$and this box is known to have a mass of 500g. We are supposed to find whether this box will float or sink in water and also the mass of water displaced by the box.
The floating and sinking of an object in water is determined by the object’s density. If the given object’s density is higher than water, it will sink and it would float if the density is found to be less than water. Density of an object is given by,
$\rho =\dfrac{M}{V}$
The density of given box,
$\rho =\dfrac{500g}{350c{{m}^{3}}}=1.42g/c{{m}^{3}}$
Now we have the density of water as $1g/c{{m}^{3}}$, which is definitely less than the box density, so the box would sink in water.
Mass of the water displaced = density of water $\times$volume of the box
$m=1g/c{{m}^{3}}\times 350c{{m}^{3}}=350g$
Therefore, we found the mass of the water displaced by the box to be 350g.

Note: If you ask me which is the law of physics that is known to be the fundamental law of fluid mechanics, I would say it is Archimedes principle. This principle states that the upward buoyant force that is being exerted on a body that is immersed in a fluid would be equal to the weight of the fluid that is displaced by the body.