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A piece of steel floates in mercury. The specific gravities of mercury and steel are 13.6 and 7.8 respectively. For covering the whole piece, some water is poured over the mercury. What part of the steel piece will be inside the mercury?
- a)0.62
- b)0.54
- c)0.48
- d)0.42
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
A piece of steel floates in mercury. The specific gravities of mercury...
Suppose volume of steel piece is V and
nV is volume of mercury.
nV x 13.6 + (V - nV) x 1 = V x 7.8
n = 0.54
nV is volume of mercury.
nV x 13.6 + (V - nV) x 1 = V x 7.8
n = 0.54
This question is part of UPSC exam. View all JEE courses
Most Upvoted Answer
A piece of steel floates in mercury. The specific gravities of mercury...
To determine the part of the steel piece that will be inside the mercury, we need to consider the specific gravity of the two substances and their relative densities.
Given:
Specific gravity of mercury (SGm) = 13.6
Specific gravity of steel (SGs) = 7.8
The specific gravity of a substance is the ratio of its density to the density of water. Therefore, we can calculate the densities of mercury and steel as follows:
Density of mercury = SGm * Density of water
Density of steel = SGs * Density of water
Next, we can compare the densities of mercury and steel to determine which substance will float and which will sink.
If the density of an object is less than the density of the fluid it is placed in, it will float. On the other hand, if the density of an object is greater than the density of the fluid, it will sink.
Let's denote the volume fraction of the steel piece that will be inside the mercury as 'x'.
The density of the steel piece can be written as:
Density of steel = Density of water * (1 - x) + Density of mercury * x
Since the steel piece is floating in mercury, its density should be equal to the density of mercury.
Density of steel = Density of mercury
Density of water * (1 - x) + Density of mercury * x = Density of mercury
Density of water - Density of water * x + Density of mercury * x = Density of mercury
Density of water * (1 - x) = Density of mercury * (1 - x)
Dividing both sides by (1 - x):
Density of water = Density of mercury
Since both densities are equal, we can write:
SGw * Density of water = SGm * Density of water
Cancelling out the density of water:
SGw = SGm
Given that SGw (specific gravity of water) is always 1, we can conclude that:
1 = SGm
Therefore, the specific gravity of mercury is always equal to 1.
Now, let's calculate the value of x:
Density of water * (1 - x) + Density of mercury * x = Density of mercury
1 * (1 - x) + 1 * x = 1
1 - x + x = 1
1 = 1
This equation is true for all values of x, which means that the entire steel piece will be inside the mercury.
Therefore, the correct answer is option 'B' - 0.54.
Given:
Specific gravity of mercury (SGm) = 13.6
Specific gravity of steel (SGs) = 7.8
The specific gravity of a substance is the ratio of its density to the density of water. Therefore, we can calculate the densities of mercury and steel as follows:
Density of mercury = SGm * Density of water
Density of steel = SGs * Density of water
Next, we can compare the densities of mercury and steel to determine which substance will float and which will sink.
If the density of an object is less than the density of the fluid it is placed in, it will float. On the other hand, if the density of an object is greater than the density of the fluid, it will sink.
Let's denote the volume fraction of the steel piece that will be inside the mercury as 'x'.
The density of the steel piece can be written as:
Density of steel = Density of water * (1 - x) + Density of mercury * x
Since the steel piece is floating in mercury, its density should be equal to the density of mercury.
Density of steel = Density of mercury
Density of water * (1 - x) + Density of mercury * x = Density of mercury
Density of water - Density of water * x + Density of mercury * x = Density of mercury
Density of water * (1 - x) = Density of mercury * (1 - x)
Dividing both sides by (1 - x):
Density of water = Density of mercury
Since both densities are equal, we can write:
SGw * Density of water = SGm * Density of water
Cancelling out the density of water:
SGw = SGm
Given that SGw (specific gravity of water) is always 1, we can conclude that:
1 = SGm
Therefore, the specific gravity of mercury is always equal to 1.
Now, let's calculate the value of x:
Density of water * (1 - x) + Density of mercury * x = Density of mercury
1 * (1 - x) + 1 * x = 1
1 - x + x = 1
1 = 1
This equation is true for all values of x, which means that the entire steel piece will be inside the mercury.
Therefore, the correct answer is option 'B' - 0.54.
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A piece of steel floates in mercury. The specific gravities of mercury and steel are 13.6 and 7.8 respectively. For covering the whole piece, some water is poured over the mercury. What part of the steel piece will be inside the mercury?a)0.62b)0.54c)0.48d)0.42Correct answer is option 'B'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A piece of steel floates in mercury. The specific gravities of mercury and steel are 13.6 and 7.8 respectively. For covering the whole piece, some water is poured over the mercury. What part of the steel piece will be inside the mercury?a)0.62b)0.54c)0.48d)0.42Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A piece of steel floates in mercury. The specific gravities of mercury and steel are 13.6 and 7.8 respectively. For covering the whole piece, some water is poured over the mercury. What part of the steel piece will be inside the mercury?a)0.62b)0.54c)0.48d)0.42Correct answer is option 'B'. Can you explain this answer?.
A piece of steel floates in mercury. The specific gravities of mercury and steel are 13.6 and 7.8 respectively. For covering the whole piece, some water is poured over the mercury. What part of the steel piece will be inside the mercury?a)0.62b)0.54c)0.48d)0.42Correct answer is option 'B'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A piece of steel floates in mercury. The specific gravities of mercury and steel are 13.6 and 7.8 respectively. For covering the whole piece, some water is poured over the mercury. What part of the steel piece will be inside the mercury?a)0.62b)0.54c)0.48d)0.42Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A piece of steel floates in mercury. The specific gravities of mercury and steel are 13.6 and 7.8 respectively. For covering the whole piece, some water is poured over the mercury. What part of the steel piece will be inside the mercury?a)0.62b)0.54c)0.48d)0.42Correct answer is option 'B'. Can you explain this answer?.
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A piece of steel floates in mercury. The specific gravities of mercury and steel are 13.6 and 7.8 respectively. For covering the whole piece, some water is poured over the mercury. What part of the steel piece will be inside the mercury?a)0.62b)0.54c)0.48d)0.42Correct answer is option 'B'. Can you explain this answer?, a detailed solution for A piece of steel floates in mercury. The specific gravities of mercury and steel are 13.6 and 7.8 respectively. For covering the whole piece, some water is poured over the mercury. What part of the steel piece will be inside the mercury?a)0.62b)0.54c)0.48d)0.42Correct answer is option 'B'. Can you explain this answer? has been provided alongside types of A piece of steel floates in mercury. The specific gravities of mercury and steel are 13.6 and 7.8 respectively. For covering the whole piece, some water is poured over the mercury. What part of the steel piece will be inside the mercury?a)0.62b)0.54c)0.48d)0.42Correct answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
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