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A student measures the distance traversed in free fall of a body, initially at rest, in a given time. He uses this data to estimate g, the acceleration due to gravity. If the maximum percentage errors in measurement of the distance and the time are e1 and e2 respectively, the percentage error in the estimation of g is
  • a)
    e2 − e1
  • b)
    e1 + 2e2
  • c)
    e1 + e2
  • d)
    e1 − 2e2
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
A student measures the distance traversed in free fall of a body, ini...
From the relation
(∵ body initially at rest)
Taking natural logarithm on both sides, we get
l n g = l n2 + l nh − 2l n t
Differentiating,
For maximum permissible error,
or
According to problem
Free Test
Community Answer
A student measures the distance traversed in free fall of a body, ini...
Percentage Error in Estimation of g

Given:
- Maximum percentage error in measurement of distance: e1
- Maximum percentage error in measurement of time: e2

Formula for Acceleration due to Gravity (g):
g = 2d/t^2
where d is the distance traversed and t is the time taken

Calculating the Percentage Error in g:
Percentage error in g = |(∂g/g) / (∂d/d) + (∂g/g) / (∂t/t)|

Calculating Partial Derivatives:
- ∂g/g = 1
- ∂d/d = e1
- ∂t/t = e2

Substitute the Values:
Percentage error in g = |1/e1 + 1/e2| = |(e1 + e2) / (e1 * e2)|

Therefore, the Percentage Error in Estimation of g is:
(e1 + e2) / (e1 * e2)

Correct Answer: Option B: e1 + 2e2
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A student measures the distance traversed in free fall of a body, initially at rest, in a given time. He uses this data to estimate g, the acceleration due to gravity. If the maximum percentage errors in measurement of the distance and the time are e1 and e2 respectively, the percentage error in the estimation of g isa)e2 − e1b)e1 + 2e2c)e1 + e2d)e1 − 2e2Correct answer is option 'B'. Can you explain this answer?
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A student measures the distance traversed in free fall of a body, initially at rest, in a given time. He uses this data to estimate g, the acceleration due to gravity. If the maximum percentage errors in measurement of the distance and the time are e1 and e2 respectively, the percentage error in the estimation of g isa)e2 − e1b)e1 + 2e2c)e1 + e2d)e1 − 2e2Correct answer is option 'B'. Can you explain this answer? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A student measures the distance traversed in free fall of a body, initially at rest, in a given time. He uses this data to estimate g, the acceleration due to gravity. If the maximum percentage errors in measurement of the distance and the time are e1 and e2 respectively, the percentage error in the estimation of g isa)e2 − e1b)e1 + 2e2c)e1 + e2d)e1 − 2e2Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A student measures the distance traversed in free fall of a body, initially at rest, in a given time. He uses this data to estimate g, the acceleration due to gravity. If the maximum percentage errors in measurement of the distance and the time are e1 and e2 respectively, the percentage error in the estimation of g isa)e2 − e1b)e1 + 2e2c)e1 + e2d)e1 − 2e2Correct answer is option 'B'. Can you explain this answer?.
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