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A given arteriole has a resistance of 2. What would the new resistance of this vessel be if its radius were to double?
- a)1
- b)1/16
- c)1/8
- d)4
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
A given arteriole has a resistance of 2. What would the new resistance...
Resistance in a tube is equal to 
, where L is the length of the tube, n is the viscosity, and r is the radius.
Therefore, the resistance is proportional to 1/r4
, where L is the length of the tube, n is the viscosity, and r is the radius.Therefore, the resistance is proportional to 1/r4
= The new resistance would be 1/8
Most Upvoted Answer
A given arteriole has a resistance of 2. What would the new resistance...
Given Information:
- Resistance of the arteriole = 2
- The radius of the arteriole doubles
To find:
- The new resistance of the arteriole after the radius doubles
Formula:
- Resistance (R) is inversely proportional to the fourth power of the radius (r) of the vessel.
- Mathematically, R ∝ 1/r^4
Solution:
1. Initial Resistance:
- According to the given information, the initial resistance of the arteriole is 2.
2. Relationship between Resistance and Radius:
- The resistance of a vessel is inversely proportional to the fourth power of its radius.
- When the radius of a vessel doubles, the resistance will change accordingly.
3. Doubling the Radius:
- Let's assume the initial radius of the arteriole is 'r'.
- When the radius doubles, the new radius becomes '2r'.
4. Relationship between Initial and New Resistance:
- According to the formula, the initial resistance is inversely proportional to the fourth power of the initial radius: R ∝ 1/r^4.
- The new resistance will be inversely proportional to the fourth power of the new radius: R' ∝ 1/(2r)^4.
5. Calculating the New Resistance:
- Substituting the new radius (2r) into the formula, we get: R' ∝ 1/(2r)^4 = 1/16r^4.
- The new resistance is 1/16 times the initial resistance.
- Therefore, the new resistance of the arteriole after the radius doubles is 1/16 of the initial resistance.
6. Answer:
- The new resistance of the arteriole after the radius doubles is 1/8 (which is equivalent to 1/16).
- Resistance of the arteriole = 2
- The radius of the arteriole doubles
To find:
- The new resistance of the arteriole after the radius doubles
Formula:
- Resistance (R) is inversely proportional to the fourth power of the radius (r) of the vessel.
- Mathematically, R ∝ 1/r^4
Solution:
1. Initial Resistance:
- According to the given information, the initial resistance of the arteriole is 2.
2. Relationship between Resistance and Radius:
- The resistance of a vessel is inversely proportional to the fourth power of its radius.
- When the radius of a vessel doubles, the resistance will change accordingly.
3. Doubling the Radius:
- Let's assume the initial radius of the arteriole is 'r'.
- When the radius doubles, the new radius becomes '2r'.
4. Relationship between Initial and New Resistance:
- According to the formula, the initial resistance is inversely proportional to the fourth power of the initial radius: R ∝ 1/r^4.
- The new resistance will be inversely proportional to the fourth power of the new radius: R' ∝ 1/(2r)^4.
5. Calculating the New Resistance:
- Substituting the new radius (2r) into the formula, we get: R' ∝ 1/(2r)^4 = 1/16r^4.
- The new resistance is 1/16 times the initial resistance.
- Therefore, the new resistance of the arteriole after the radius doubles is 1/16 of the initial resistance.
6. Answer:
- The new resistance of the arteriole after the radius doubles is 1/8 (which is equivalent to 1/16).
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A given arteriole has a resistance of 2. What would the new resistance of this vessel be if its radius were to double?a)1b)1/16c)1/8d)4Correct answer is option 'C'. Can you explain this answer? for MCAT 2025 is part of MCAT preparation. The Question and answers have been prepared according to the MCAT exam syllabus. Information about A given arteriole has a resistance of 2. What would the new resistance of this vessel be if its radius were to double?a)1b)1/16c)1/8d)4Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for MCAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A given arteriole has a resistance of 2. What would the new resistance of this vessel be if its radius were to double?a)1b)1/16c)1/8d)4Correct answer is option 'C'. Can you explain this answer?.
A given arteriole has a resistance of 2. What would the new resistance of this vessel be if its radius were to double?a)1b)1/16c)1/8d)4Correct answer is option 'C'. Can you explain this answer? for MCAT 2025 is part of MCAT preparation. The Question and answers have been prepared according to the MCAT exam syllabus. Information about A given arteriole has a resistance of 2. What would the new resistance of this vessel be if its radius were to double?a)1b)1/16c)1/8d)4Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for MCAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A given arteriole has a resistance of 2. What would the new resistance of this vessel be if its radius were to double?a)1b)1/16c)1/8d)4Correct answer is option 'C'. Can you explain this answer?.
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