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Quantitative Reasoning – Passage Based – Density and Plimsoll line!

PSA 2014_XI_Q11. Read the following passage and answer the questions that follow:

All substance, whether they are solids, liquids or gases, are made up of particles. The density of a substance depends upon how close together its particles are. Solid substances usually have high densities because their particles are very close together while gases, which have large spaces between their particles, have very low densities. Density can be calculated by dividing the mass (in grams) by its volume (in cubic centimetres). The table below shows the densities of different substances.

PSA 2014_XI_Q11_1

Objects will float in water if they have a density that is equal to, or lower than, the density of water. A piece of cork floats in water because cork has a lower density than water. A steel nail, which has a density about 8 times that of water, sinks.
Steel ships are able to float because they are not solid pieces of metal like a nail. A ship’s hull is actually a steel shell filled mostly with air which is very light. As a result, the total mass of the ship is very low compared to its volume so it has a smaller average density. This average density is lower than that of water and so the ship floats.

As cargo is added to a ship, it sinks lower down into the water. Ships also float at different levels depending on the temperature of the water and whether it is fresh water or seawater. This is because the densities of warm water and cold water are different. The density of salt water is also different to the density of freshwater.
The Plimsoll line shown below is a marking that can be found on the hulls of ships to indicate the safe level to which the ship can be loaded in different types of water.

PSA 2014_XI_Q11_2

(i)Which of the following statements is true ?
1) Salt water is less dense than fresh water.
2) Warm water is denser than cool water.
3) A ship will sit lower in the water in winter than in summer
4) A ship that is loaded in freshwater will rise when it enters an ocean.

(ii)What is the mass of 1 litre of air ?
1) 1.29
2) 0.12 g
3) 0.0012 g
4) 0.012 kg

(iii) Why does a ship sink when a large enough hole has been torn in its hull and water enters the ship ?
1) Its mass and the volume of its hull have increased.
2) Its mass has decreased and the volume of its hull has increased.
3) Its mass remains the same but the volume of its hull has decreased.
4) Its mass has increased while the volume of its hull remains the same.

Liquids that have different densities form layers. The liquid with the lowest density floats at the top and the
densest liquid sinks to the bottom. The diagram below shows 3 containers. Each container holds two different
liquids. In total, 4 different liquids are shown.

PSA 2014_XI_Q11_3

(iv) This diagram proves that
1) Liquid B has the highest density.
2) Liquid D has the lowest density.
3) Liquid C has a higher density than B.
a) Liquid B is more dense than either liquid A or liquid C.

Ans: 

(i) Let us look at each of the options:

(1)Salt water is less dense than fresh water –> Wrong, just the opposite is true.
(2) Warm water is denser than cool water –> Warm water is less dense.
(3) A ship will sit lower in the water in winter than in summer -> In winter water density would increase, this will cause ship to rise.
(4)A ship that is loaded in fresh water will rise when it enters an ocean -> This is correct as ocean water has higher density than fresh water.

Option 4.

(ii) The density of air is given as 0.0012 gm/cm3. 1 cubic cm= 0.001lt.

0.001 lt contains 0.0012 gm of air.
1 lt contains 0.0012/0.001 gm= 1.2 gm. Option (1)

(iii) When a large enough hole has been torn in its hull and water enters the ship, the mass of the ship increases. Volume remains the same as there is no change in dimensions of hull. Overall average density increases as water fills in the hull. The ship sinks when the average density of the ship increases that of the water it displaces.
Option (4)

(iv) From the first container, Density of B < Density of A
From the second container, Density of A < Density of C

Therefore, Density of B < Density of A < Density of C –(G)

From the third container, Density of B < Density of D.

1) Liquid B has the highest density –> Wrong. In fact it has the lowest.
2) Liquid D has the lowest density –> Wrong, density of B is lowest.
3) Liquid C has a higher density than B. –> True.
a) Liquid B is more dense than either liquid A or liquid C. –> Wrong

Only option (3) is correct.

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