A container is first filled with water and then the entire water is re

A container is first filled with water and then the entire water is replaced by mercury. Mercury has a density of 13·6 × 10³ kg/m³. If X is the weight of the water and Y is the weight of the mercury, then

X = Y
X = 13·6 Y
Y = 13·6 X
None of the above
This question was previously asked in
UPSC NDA-1 – 2016
The weight of an object is given by W = m * g, where m is the mass and g is the acceleration due to gravity. The mass of a substance filling a container of volume V is given by m = ρ * V, where ρ is the density of the substance.
For water, the weight X is given by X = ρwater * V * g.
For mercury, the weight Y is given by Y = ρmercury * V * g.
The density of water is approximately 1.0 × 10³ kg/m³.
The density of mercury is given as 13.6 × 10³ kg/m³.
Taking the ratio of the weights:
Y / X = (ρmercury * V * g) / (ρwater * V * g)
Y / X = ρmercury / ρwater
Y / X = (13.6 × 10³) / (1.0 × 10³) = 13.6
Therefore, Y = 13.6 X.
Weight depends on mass and gravitational acceleration. Mass is proportional to density for a fixed volume. The ratio of weights for the same volume of different substances is equal to the ratio of their densities.
The density of water varies slightly with temperature and pressure, but 1000 kg/m³ is a standard value at 4°C. The acceleration due to gravity (g) is the same for both substances in the same location, so it cancels out in the ratio.