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A man grows into a giant such that his linear dimensions increase by a factor of 9. Assuming that his density remains same, the stress in the leg will change by a factor of
- a)81
- b)1/81
- c)9
- d)1/9
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
A man grows into a giant such that his linear dimensions increase by a...
∵ Density remains same
So, mass ∝ Volume
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A man grows into a giant such that his linear dimensions increase by a...
Given Information:
A man grows into a giant such that his linear dimensions increase by a factor of 9. The density of the man remains the same.
To Find:
The factor by which the stress in the leg changes.
Solution:
1. Relationship between Stress and Pressure:
Stress is defined as force per unit area. It is given by the equation:
Stress = Force / Area
Pressure is defined as force per unit area. It is given by the equation:
Pressure = Force / Area
Since stress and pressure have the same units and are defined in the same way, they are equal.
2. Relationship between Pressure and Volume:
Pressure is inversely proportional to volume, given by the equation:
Pressure ∝ 1 / Volume
3. Relationship between Volume and Linear Dimensions:
Volume is directly proportional to the cube of linear dimensions, given by the equation:
Volume ∝ (Linear Dimensions)^3
4. Relationship between Pressure and Density:
Pressure is directly proportional to density, given by the equation:
Pressure ∝ Density
5. Applying the Relationships:
Since the linear dimensions of the man increase by a factor of 9, the volume of the man will increase by a factor of (9^3) = 729.
Since the density of the man remains the same, the pressure in the leg will increase by a factor of 729.
Therefore, the stress in the leg will also increase by a factor of 729.
6. Answer:
The factor by which the stress in the leg changes is 729, which can be written as 9^3.
Therefore, the correct answer is option C) 9.
A man grows into a giant such that his linear dimensions increase by a factor of 9. The density of the man remains the same.
To Find:
The factor by which the stress in the leg changes.
Solution:
1. Relationship between Stress and Pressure:
Stress is defined as force per unit area. It is given by the equation:
Stress = Force / Area
Pressure is defined as force per unit area. It is given by the equation:
Pressure = Force / Area
Since stress and pressure have the same units and are defined in the same way, they are equal.
2. Relationship between Pressure and Volume:
Pressure is inversely proportional to volume, given by the equation:
Pressure ∝ 1 / Volume
3. Relationship between Volume and Linear Dimensions:
Volume is directly proportional to the cube of linear dimensions, given by the equation:
Volume ∝ (Linear Dimensions)^3
4. Relationship between Pressure and Density:
Pressure is directly proportional to density, given by the equation:
Pressure ∝ Density
5. Applying the Relationships:
Since the linear dimensions of the man increase by a factor of 9, the volume of the man will increase by a factor of (9^3) = 729.
Since the density of the man remains the same, the pressure in the leg will increase by a factor of 729.
Therefore, the stress in the leg will also increase by a factor of 729.
6. Answer:
The factor by which the stress in the leg changes is 729, which can be written as 9^3.
Therefore, the correct answer is option C) 9.
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A man grows into a giant such that his linear dimensions increase by a factor of 9. Assuming that his density remains same, the stress in the leg will change by a factor ofa)81b)1/81c)9d)1/9Correct answer is option 'C'. Can you explain this answer?
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A man grows into a giant such that his linear dimensions increase by a factor of 9. Assuming that his density remains same, the stress in the leg will change by a factor ofa)81b)1/81c)9d)1/9Correct answer is option 'C'. 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 man grows into a giant such that his linear dimensions increase by a factor of 9. Assuming that his density remains same, the stress in the leg will change by a factor ofa)81b)1/81c)9d)1/9Correct answer is option 'C'. 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 man grows into a giant such that his linear dimensions increase by a factor of 9. Assuming that his density remains same, the stress in the leg will change by a factor ofa)81b)1/81c)9d)1/9Correct answer is option 'C'. Can you explain this answer?.
A man grows into a giant such that his linear dimensions increase by a factor of 9. Assuming that his density remains same, the stress in the leg will change by a factor ofa)81b)1/81c)9d)1/9Correct answer is option 'C'. 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 man grows into a giant such that his linear dimensions increase by a factor of 9. Assuming that his density remains same, the stress in the leg will change by a factor ofa)81b)1/81c)9d)1/9Correct answer is option 'C'. 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 man grows into a giant such that his linear dimensions increase by a factor of 9. Assuming that his density remains same, the stress in the leg will change by a factor ofa)81b)1/81c)9d)1/9Correct answer is option 'C'. Can you explain this answer?.
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