Question

A boy is carrying a bucket of water in one hand and a piece of plastic in the other. After transferring the piece of plastic to the bucket (in which it floats) the boy will carry
(a). same load as before
(b). more load as before

Answer 1

Hint: When the plastic piece is transferred into the bucket of water, there are some forces acting on the object. One of those forces is buoyant force which is due to the pressure inside the water and is also the reason why the piece of plastic floats on water rather than sinking.

Formula used:
\[W=mg\]
\[{{F}_{b}}=-\rho gV\]

Complete step by step solution:
Buoyant force (\[{{F}_{b}}\] )is an upward force acting on a body partially or fully submerged in a fluid. It is also called upthrust force. For a column of fluid, as we go deeper, the pressure increases because of the fluid over it. Therefore, the pressure at the top of a column is greater than the pressure at the bottom of a column. This pressure difference is responsible for a net upward force on the object and this force is proportional to the pressure difference.
\[{{F}_{b}}\propto {{P}_{b}}-{{P}_{a}}\]
Here, \[{{P}_{b}}\] is the pressure at the bottom of the fluid column
\[{{P}_{a}}\] is the pressure at the top of the fluid column.
 \[{{F}_{b}}\]is also proportional to the weight of the displaced fluid, i.e., fluid equivalent to the space occupied by the submerged object.
That is why; objects that have a density greater than the fluid tend to sink while objects that are less dense tend to float.
In the question, after the boy transfers the piece of plastic in the bucket of water. Two forces acting on the piece are-
Weight of plastic \[W=mg\] (\[m\] is the mass of plastic piece, \[g\] is the acceleration due to gravity)
Buoyant force \[{{F}_{b}}=-\rho gV\] (\[\rho \] is the fluid density, \[g\]is the acceleration due to gravity, \[V\] is fluid volume)
\[{{F}_{b}}\]cancels out \[W\]due to which the piece can float on water. Therefore, the boy only feels the weight of the bucket of water and not the piece of plastic so the load remains the same.
Since the load does not change, the correct option is (a).

So, the correct answer is “Option A”.

Note: When an object is submerged in a liquid, the liquid exerts pressure on it from all sides. The liquid inside a container also exerts pressure on the walls of the container from all the sides. Archimedes’ principle states that the buoyant force acting on an object is equivalent to the weight of fluid dispersed by it.