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The relative error in a physical quantity raised to the power k is.
- a)(k – 1) times the absolute error in the individual quantity
- b)(k – 1) times the relative error in the individual quantity
- c)k times the relative error in the individual quantity
- d)k times the absolute error in the individual quantity
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
The relative error in a physical quantity raised to the power k is.a)(...
The relative error in a physical quantity raised to the power k is the k times the relative error in the individual quantity.
Suppose Z = A^2,
Then,
ΔZ/Z = (ΔA/A) + (ΔA/A) = 2 (ΔA/A).
Hence, the relative error in A^2 is two times the error in A.
In general, if Z = (A^p B^q)/C^r
Then,
ΔZ/Z = p (ΔA/A) + q (ΔB/B) + r (ΔC/C).
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The relative error in a physical quantity raised to the power k is.a)(...
Explanation:
When we measure a physical quantity, there is always some amount of error involved due to various factors such as instrument limitations, human error, environmental factors, etc. This error can be expressed in terms of absolute error or relative error.
Absolute error is the difference between the measured value and the true value of a quantity, while relative error is the ratio of the absolute error to the true value of the quantity.
When we raise a physical quantity to the power k, the error associated with it also gets raised to the power k. This means that the relative error in the final result will depend on the relative error in the individual quantity and the power to which it is raised.
To calculate the relative error in the final result, we can use the following formula:
Relative error in final result = k x relative error in individual quantity
This formula tells us that the relative error in the final result is directly proportional to the power to which the quantity is raised and the relative error in the individual quantity.
Therefore, the correct option is C, which states that the relative error in a physical quantity raised to the power k is k times the relative error in the individual quantity.
When we measure a physical quantity, there is always some amount of error involved due to various factors such as instrument limitations, human error, environmental factors, etc. This error can be expressed in terms of absolute error or relative error.
Absolute error is the difference between the measured value and the true value of a quantity, while relative error is the ratio of the absolute error to the true value of the quantity.
When we raise a physical quantity to the power k, the error associated with it also gets raised to the power k. This means that the relative error in the final result will depend on the relative error in the individual quantity and the power to which it is raised.
To calculate the relative error in the final result, we can use the following formula:
Relative error in final result = k x relative error in individual quantity
This formula tells us that the relative error in the final result is directly proportional to the power to which the quantity is raised and the relative error in the individual quantity.
Therefore, the correct option is C, which states that the relative error in a physical quantity raised to the power k is k times the relative error in the individual quantity.
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The relative error in a physical quantity raised to the power k is.a)(k – 1) times the absolute error in the individual quantityb)(k – 1) times the relative error in the individual quantityc)k times the relative error in the individual quantityd)k times the absolute error in the individual quantityCorrect answer is option 'C'. Can you explain this answer?
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