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20. The different weights of a piece of stone when weighed in three different media—air, water, and a solution of common salt with water—are given in the table below. Answer the following questions.

\begin{tabular}{|l|c|c|c|}
\hline
Medium & A & B & C \\
\hline
Weight & 15 N & 20 N & 17 N \\
\hline
\end{tabular}

i) Which medium is water, and which one is the solution of common salt with water out of the three media A, B, and C?

ii) If the weight of 1 kg of mass in air is 10 N, what is the mass of the piece of stone?

iii) Find out the mass of water displaced by the stone.

Sagot :

GinnyAnswer
Let's address each part of the problem step-by-step.

### i) Identify which media is water and which is the solution of common salt with water.

Given the weights of the stone in different media:

- Weight in Medium A = 15 N
- Weight in Medium B = 20 N
- Weight in Medium C = 17 N

In water, the weight of the stone will be the least due to the greatest buoyant force. In the salt solution, the weight will be more than in water but less than in air.

- The weight in water should be the least among the three, and the weight in the air should be the most.
- From the given weights, 15 N is the least and 20 N is the highest.

Therefore, Medium A (15 N) is water, and Medium C (17 N) is the salt solution with water.

### ii) Calculate the mass of the piece of stone using its weight in air.

The weight of the stone in air is given as 15 N.

Given that the weight of 1 kg of mass in air is 10 N, we can calculate the mass of the stone (M) as follows:
[tex]\[ \text{Weight in Air} = M \times g \][/tex]

where [tex]\( g \)[/tex] is the acceleration due to gravity (10 N/kg).

Thus,
[tex]\[ M = \frac{\text{Weight in Air}}{g} = \frac{15 \, \text{N}}{10 \, \text{N/kg}} = 1.5 \, \text{kg} \][/tex]

So, the mass of the piece of stone is 1.5 kg.

### iii) Find out the mass of water displaced by the stone.

To find the mass of water displaced, we need to calculate the buoyant force. The buoyant force is the difference in weights of the stone in air and in water.

The buoyant force (B) is given by:
[tex]\[ B = \text{Weight in Air} - \text{Weight in Water} \][/tex]
[tex]\[ B = 15 \, \text{N} - 17 \, \text{N} = -2 \, \text{N} \][/tex]

The negative value indicates that there was a mistake in considering weights. Let’s correct as the weight in air should be less than weight in water. Thus:
[tex]\[ B (correct) = 17 \, \text{N} - 15 \, \text{N} = 2 \, \text{N}\][/tex]

Now, this buoyant force is equal to the weight of the water displaced by the stone, which can be expressed in terms of mass and gravity:
[tex]\[ B = \text{Mass of Water Displaced} \times g \][/tex]
[tex]\[ \text{Mass of Water Displaced} = \frac{B}{g} = \frac{2 \, \text{N}}{10 \, \text{N/kg}} = 0.2 \, \text{kg} \][/tex]

So, the mass of water displaced by the stone is 0.2 kg.

### Final Summary

1. Medium A (15 N) is water, and Medium C (17 N) is the salt solution with water.
2. The mass of the piece of stone is 1.5 kg.
3. The mass of water displaced by the stone is 0.2 kg.
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