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It is given that a is equal to b square if a is equal to 20 ±0.01 then b is equal to 1.00±0.01 cm . the given AB is ?
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It is given that a is equal to b square if a is equal to 20 ±0.01 then...
Understanding the Relationship Between a and b
Given that \( a = b^2 \), we can derive the value of \( b \) from the provided information about \( a \).
Given Values:
- \( a = 20 \pm 0.01 \)
To find \( b \), we need to solve for \( b \):
\[
b = \sqrt{a}
\]
Calculating the Central Value of b:
- Substituting \( a \):
\[
b = \sqrt{20} \approx 4.47
\]
Calculating the Uncertainty in b:
To find the uncertainty in \( b \), we use the formula for propagation of uncertainty:
\[
\Delta b = \frac{1}{2\sqrt{a}} \cdot \Delta a
\]
Where:
- \( \Delta a = 0.01 \)
Substituting the values:
\[
\Delta b = \frac{1}{2\sqrt{20}} \cdot 0.01 \approx \frac{1}{2 \cdot 4.47} \cdot 0.01 \approx 0.00112
\]
Rounding off gives us:
\[
\Delta b \approx 0.01
\]
Final Value of b:
Thus, the value of \( b \) can be expressed as:
\[
b \approx 4.47 \pm 0.01
\]
Conclusion:
In summary, when \( a \) is \( 20 \pm 0.01 \), we find:
- \( b \) is approximately \( 4.47 \pm 0.01 \) cm.
This demonstrates how to effectively use the relationship between two variables and the propagation of uncertainties to arrive at a final value.
Given that \( a = b^2 \), we can derive the value of \( b \) from the provided information about \( a \).
Given Values:
- \( a = 20 \pm 0.01 \)
To find \( b \), we need to solve for \( b \):
\[
b = \sqrt{a}
\]
Calculating the Central Value of b:
- Substituting \( a \):
\[
b = \sqrt{20} \approx 4.47
\]
Calculating the Uncertainty in b:
To find the uncertainty in \( b \), we use the formula for propagation of uncertainty:
\[
\Delta b = \frac{1}{2\sqrt{a}} \cdot \Delta a
\]
Where:
- \( \Delta a = 0.01 \)
Substituting the values:
\[
\Delta b = \frac{1}{2\sqrt{20}} \cdot 0.01 \approx \frac{1}{2 \cdot 4.47} \cdot 0.01 \approx 0.00112
\]
Rounding off gives us:
\[
\Delta b \approx 0.01
\]
Final Value of b:
Thus, the value of \( b \) can be expressed as:
\[
b \approx 4.47 \pm 0.01
\]
Conclusion:
In summary, when \( a \) is \( 20 \pm 0.01 \), we find:
- \( b \) is approximately \( 4.47 \pm 0.01 \) cm.
This demonstrates how to effectively use the relationship between two variables and the propagation of uncertainties to arrive at a final value.
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It is given that a is equal to b square if a is equal to 20 ±0.01 then b is equal to 1.00±0.01 cm . the given AB is ? for NEET 2025 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about It is given that a is equal to b square if a is equal to 20 ±0.01 then b is equal to 1.00±0.01 cm . the given AB is ? covers all topics & solutions for NEET 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for It is given that a is equal to b square if a is equal to 20 ±0.01 then b is equal to 1.00±0.01 cm . the given AB is ?.
It is given that a is equal to b square if a is equal to 20 ±0.01 then b is equal to 1.00±0.01 cm . the given AB is ? for NEET 2025 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about It is given that a is equal to b square if a is equal to 20 ±0.01 then b is equal to 1.00±0.01 cm . the given AB is ? covers all topics & solutions for NEET 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for It is given that a is equal to b square if a is equal to 20 ±0.01 then b is equal to 1.00±0.01 cm . the given AB is ?.
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