Question

A block of wood with a metal plate placed on its top floats in water as shown in figure, with x = $2\,cm$ and y = $50\,cm$ , the possible value of $x$ and $y$ after the metal plate has fallen in water.

A. $3,52$
B. $3,49$
C. $1,51$
D. $1,48$

Answer 1

To solve these types of questions, we need to know the concepts of buoyancy and buoyant force and how density of materials and density of bodies in the liquid are related (Archimedes’ principle). WE have been given the coordinate of the material immersed in the liquid, with some weight added on it, we just have to determine its new coordinates, by the use of the concept of buoyant force.

Complete step by step answer:
By Archimedes’ principle, we see that the volume of a body immersed in a fluid is proportional to its density. Now this density and weight of the body are related and thus we can say that the volume of the immersed body is related to its weight.

We can say at the given condition, we have two bodies, and at the final condition, as the metal plate falls in water, the weight over the wooden block is decreased and as a result of it, the volume immersed in the water also gets decreased. This is due to the lowering of the buoyant force and is in accordance with Archimedes' principle.

Thus as a result of it, the volume immersed gets decreased, now in-order to decrease the immersed volume, the three dimensions need to change, but we see the base of the wooden block remains in contact with the dimension, thus the value of x and y respectively decreases from the initial value of $3 cm$ and $50 cm$ respectively.

Hence, the correct answer is option D.

Note: These questions require just the general understanding and concept of buoyancy. Remember that the density is always compared to see whether an object floats on the surface of a given liquid. Also, remember how mass and density are interrelated.