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PARAGRAPH “A”
If the measurement errors in all the independent quantities are known, then it is possible to determine the error in any dependent quantity. This is done by the use of series expansion and truncating the expansion at the first power of the error. For example, consider the relation z = x/y. If the errors in x, y and z are Δx, Δy and Δz, respectively, then
. The series expansion for  to first power in Δy/y is   The relative errors in independent variables are always added. So the error in z will be

The above derivation makes the assumption that Δx/x << 1, Δy/y << 1,  Therefore, the higher powers of these quantities are neglected.
Q. Consider the ratio  to be determined by measuring a dimensionless quantity a. If the error in the measurement of a is  then what is the error Δr in determining r?
  • a)
  • b)
  • c)
  • d)
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
PARAGRAPH “A”If the measurement errors in all the independ...
The ratio is,

For small error,

The expression for the magnitude of the error in r is,
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PARAGRAPH “A”If the measurement errors in all the independent quantities are known, then it is possible to determine the error in any dependent quantity. This is done by the use of series expansion and truncating the expansion at the first power of the error. For example, consider the relation z = x/y. If the errors in x, y and z are Δx, Δy and Δz, respectively, then.The series expansion forto first power inΔy/yisThe relative errors in independent variables are always added. So the error in z will beThe above derivation makes the assumption thatΔx/x << 1,Δy/y<< 1,Therefore, the higher powers of these quantities areneglected.Q.Consider the ratioto be determined by measuring adimensionless quantity a.If the error in the measurement of a isthen what is the error Δrin determining r?a)b)c)d)Correct answer is option 'B'. Can you explain this answer?
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PARAGRAPH “A”If the measurement errors in all the independent quantities are known, then it is possible to determine the error in any dependent quantity. This is done by the use of series expansion and truncating the expansion at the first power of the error. For example, consider the relation z = x/y. If the errors in x, y and z are Δx, Δy and Δz, respectively, then.The series expansion forto first power inΔy/yisThe relative errors in independent variables are always added. So the error in z will beThe above derivation makes the assumption thatΔx/x << 1,Δy/y<< 1,Therefore, the higher powers of these quantities areneglected.Q.Consider the ratioto be determined by measuring adimensionless quantity a.If the error in the measurement of a isthen what is the error Δrin determining r?a)b)c)d)Correct answer is option 'B'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about PARAGRAPH “A”If the measurement errors in all the independent quantities are known, then it is possible to determine the error in any dependent quantity. This is done by the use of series expansion and truncating the expansion at the first power of the error. For example, consider the relation z = x/y. If the errors in x, y and z are Δx, Δy and Δz, respectively, then.The series expansion forto first power inΔy/yisThe relative errors in independent variables are always added. So the error in z will beThe above derivation makes the assumption thatΔx/x << 1,Δy/y<< 1,Therefore, the higher powers of these quantities areneglected.Q.Consider the ratioto be determined by measuring adimensionless quantity a.If the error in the measurement of a isthen what is the error Δrin determining r?a)b)c)d)Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for PARAGRAPH “A”If the measurement errors in all the independent quantities are known, then it is possible to determine the error in any dependent quantity. This is done by the use of series expansion and truncating the expansion at the first power of the error. For example, consider the relation z = x/y. If the errors in x, y and z are Δx, Δy and Δz, respectively, then.The series expansion forto first power inΔy/yisThe relative errors in independent variables are always added. So the error in z will beThe above derivation makes the assumption thatΔx/x << 1,Δy/y<< 1,Therefore, the higher powers of these quantities areneglected.Q.Consider the ratioto be determined by measuring adimensionless quantity a.If the error in the measurement of a isthen what is the error Δrin determining r?a)b)c)d)Correct answer is option 'B'. Can you explain this answer?.
Solutions for PARAGRAPH “A”If the measurement errors in all the independent quantities are known, then it is possible to determine the error in any dependent quantity. This is done by the use of series expansion and truncating the expansion at the first power of the error. For example, consider the relation z = x/y. If the errors in x, y and z are Δx, Δy and Δz, respectively, then.The series expansion forto first power inΔy/yisThe relative errors in independent variables are always added. So the error in z will beThe above derivation makes the assumption thatΔx/x << 1,Δy/y<< 1,Therefore, the higher powers of these quantities areneglected.Q.Consider the ratioto be determined by measuring adimensionless quantity a.If the error in the measurement of a isthen what is the error Δrin determining r?a)b)c)d)Correct answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE. Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free.
Here you can find the meaning of PARAGRAPH “A”If the measurement errors in all the independent quantities are known, then it is possible to determine the error in any dependent quantity. This is done by the use of series expansion and truncating the expansion at the first power of the error. For example, consider the relation z = x/y. If the errors in x, y and z are Δx, Δy and Δz, respectively, then.The series expansion forto first power inΔy/yisThe relative errors in independent variables are always added. So the error in z will beThe above derivation makes the assumption thatΔx/x << 1,Δy/y<< 1,Therefore, the higher powers of these quantities areneglected.Q.Consider the ratioto be determined by measuring adimensionless quantity a.If the error in the measurement of a isthen what is the error Δrin determining r?a)b)c)d)Correct answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of PARAGRAPH “A”If the measurement errors in all the independent quantities are known, then it is possible to determine the error in any dependent quantity. This is done by the use of series expansion and truncating the expansion at the first power of the error. For example, consider the relation z = x/y. If the errors in x, y and z are Δx, Δy and Δz, respectively, then.The series expansion forto first power inΔy/yisThe relative errors in independent variables are always added. So the error in z will beThe above derivation makes the assumption thatΔx/x << 1,Δy/y<< 1,Therefore, the higher powers of these quantities areneglected.Q.Consider the ratioto be determined by measuring adimensionless quantity a.If the error in the measurement of a isthen what is the error Δrin determining r?a)b)c)d)Correct answer is option 'B'. Can you explain this answer?, a detailed solution for PARAGRAPH “A”If the measurement errors in all the independent quantities are known, then it is possible to determine the error in any dependent quantity. This is done by the use of series expansion and truncating the expansion at the first power of the error. For example, consider the relation z = x/y. If the errors in x, y and z are Δx, Δy and Δz, respectively, then.The series expansion forto first power inΔy/yisThe relative errors in independent variables are always added. So the error in z will beThe above derivation makes the assumption thatΔx/x << 1,Δy/y<< 1,Therefore, the higher powers of these quantities areneglected.Q.Consider the ratioto be determined by measuring adimensionless quantity a.If the error in the measurement of a isthen what is the error Δrin determining r?a)b)c)d)Correct answer is option 'B'. Can you explain this answer? has been provided alongside types of PARAGRAPH “A”If the measurement errors in all the independent quantities are known, then it is possible to determine the error in any dependent quantity. This is done by the use of series expansion and truncating the expansion at the first power of the error. For example, consider the relation z = x/y. If the errors in x, y and z are Δx, Δy and Δz, respectively, then.The series expansion forto first power inΔy/yisThe relative errors in independent variables are always added. So the error in z will beThe above derivation makes the assumption thatΔx/x << 1,Δy/y<< 1,Therefore, the higher powers of these quantities areneglected.Q.Consider the ratioto be determined by measuring adimensionless quantity a.If the error in the measurement of a isthen what is the error Δrin determining r?a)b)c)d)Correct answer is option 'B'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice PARAGRAPH “A”If the measurement errors in all the independent quantities are known, then it is possible to determine the error in any dependent quantity. This is done by the use of series expansion and truncating the expansion at the first power of the error. For example, consider the relation z = x/y. If the errors in x, y and z are Δx, Δy and Δz, respectively, then.The series expansion forto first power inΔy/yisThe relative errors in independent variables are always added. So the error in z will beThe above derivation makes the assumption thatΔx/x << 1,Δy/y<< 1,Therefore, the higher powers of these quantities areneglected.Q.Consider the ratioto be determined by measuring adimensionless quantity a.If the error in the measurement of a isthen what is the error Δrin determining r?a)b)c)d)Correct answer is option 'B'. Can you explain this answer? tests, examples and also practice JEE tests.
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