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
[amp_mcq option1=”X = Y” option2=”X = 13·6 Y” option3=”Y = 13·6 X” option4=”None of the above” correct=”option3″]
This question was previously asked in
UPSC NDA-1 – 2016
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.