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A student measures the distance covered and time taken by a body under free fall which was intially at rest. He uses this data for estimating g, the acceleration due to gravity. If the maximum percentage error in measurement of the distance and the time are e1 and e2 respectively, then the maximum possible 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?
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Verified Answer
A student measures the distance covered and time taken by a body under...
From the releation
h= 1/2gt2 ⇒ g = 2h/t2
h= 1/2gt2 ⇒ g = 2h/t2
Taking natural logarithms on both sides, we get
ln (g) = ln (h) - 2ln (t) + ln (2)
Differentiating
for maximum permissible errors , we add both the errors . so
Most Upvoted Answer
A student measures the distance covered and time taken by a body under...
To understand why the maximum possible percentage error in the estimation of g is e1 + 2e2, let's break down the problem step by step:
1. Understanding the Formula:
The formula for the distance covered by a body under free fall starting from rest is given by:
d = (1/2)gt^2
Where:
d = distance covered
g = acceleration due to gravity
t = time taken
2. Maximum Percentage Error in Distance Measurement:
Let's assume the maximum percentage error in the measurement of distance is e1. This means that the actual distance covered (d_actual) and the measured distance (d_measured) are related as follows:
d_measured = (1 + e1) * d_actual
3. Maximum Percentage Error in Time Measurement:
Similarly, let's assume the maximum percentage error in the measurement of time is e2. This means that the actual time taken (t_actual) and the measured time (t_measured) are related as follows:
t_measured = (1 + e2) * t_actual
4. Estimating g using the data:
Now, let's substitute the expressions for d_measured and t_measured in the formula for distance:
d_measured = (1 + e1) * d_actual
t_measured = (1 + e2) * t_actual
Substituting these values in the formula for distance, we get:
(1 + e1) * d_actual = (1/2)g * (1 + e2) * t_actual^2
Simplifying the equation, we have:
d_actual = (1/2)g * (1 + e2) * t_actual^2 / (1 + e1)
5. Maximum Possible Percentage Error in g:
To find the maximum possible percentage error in the estimation of g, we need to find the ratio of the maximum possible error in g (e_g) to the actual value of g:
e_g = (g_measured - g_actual) / g_actual
Substituting the expressions for d_actual and t_actual in terms of measured values, we get:
e_g = ((1 + e1) * d_measured / ((1/2) * (1 + e2) * t_measured^2)) - g_actual) / g_actual
Simplifying the equation, we have:
e_g = ((1 + e1) * d_measured / ((1/2) * (1 + e2) * t_measured^2)) - 1
Now, let's substitute the expressions for d_measured and t_measured, and simplify further:
e_g = ((1 + e1) * (1 + e2) * d_actual / ((1/2) * (1 + e2) * t_actual^2)) - 1
Cancelling out the common terms, we get:
e_g = (1 + e1) * (2/t_actual^2) - 1
e_g = (2 + 2e1 - t_actual^2) / t_actual^2
Since t_actual^2 is always positive, the maximum value of e_g occurs when t_actual^2 is at its minimum value, which is 0. Therefore, the maximum possible value of e_g is:
e_g = (2 + 2e1 - 0) / 0
1. Understanding the Formula:
The formula for the distance covered by a body under free fall starting from rest is given by:
d = (1/2)gt^2
Where:
d = distance covered
g = acceleration due to gravity
t = time taken
2. Maximum Percentage Error in Distance Measurement:
Let's assume the maximum percentage error in the measurement of distance is e1. This means that the actual distance covered (d_actual) and the measured distance (d_measured) are related as follows:
d_measured = (1 + e1) * d_actual
3. Maximum Percentage Error in Time Measurement:
Similarly, let's assume the maximum percentage error in the measurement of time is e2. This means that the actual time taken (t_actual) and the measured time (t_measured) are related as follows:
t_measured = (1 + e2) * t_actual
4. Estimating g using the data:
Now, let's substitute the expressions for d_measured and t_measured in the formula for distance:
d_measured = (1 + e1) * d_actual
t_measured = (1 + e2) * t_actual
Substituting these values in the formula for distance, we get:
(1 + e1) * d_actual = (1/2)g * (1 + e2) * t_actual^2
Simplifying the equation, we have:
d_actual = (1/2)g * (1 + e2) * t_actual^2 / (1 + e1)
5. Maximum Possible Percentage Error in g:
To find the maximum possible percentage error in the estimation of g, we need to find the ratio of the maximum possible error in g (e_g) to the actual value of g:
e_g = (g_measured - g_actual) / g_actual
Substituting the expressions for d_actual and t_actual in terms of measured values, we get:
e_g = ((1 + e1) * d_measured / ((1/2) * (1 + e2) * t_measured^2)) - g_actual) / g_actual
Simplifying the equation, we have:
e_g = ((1 + e1) * d_measured / ((1/2) * (1 + e2) * t_measured^2)) - 1
Now, let's substitute the expressions for d_measured and t_measured, and simplify further:
e_g = ((1 + e1) * (1 + e2) * d_actual / ((1/2) * (1 + e2) * t_actual^2)) - 1
Cancelling out the common terms, we get:
e_g = (1 + e1) * (2/t_actual^2) - 1
e_g = (2 + 2e1 - t_actual^2) / t_actual^2
Since t_actual^2 is always positive, the maximum value of e_g occurs when t_actual^2 is at its minimum value, which is 0. Therefore, the maximum possible value of e_g is:
e_g = (2 + 2e1 - 0) / 0
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A student measures the distance covered and time taken by a body under...
B
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A student measures the distance covered and time taken by a body under free fall which was intially at rest. He uses this data for estimating g, the acceleration due to gravity. If the maximum percentage error in measurement of the distance and the time are e1 and e2respectively, then the maximum possible 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 covered and time taken by a body under free fall which was intially at rest. He uses this data for estimating g, the acceleration due to gravity. If the maximum percentage error in measurement of the distance and the time are e1 and e2respectively, then the maximum possible 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 Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about A student measures the distance covered and time taken by a body under free fall which was intially at rest. He uses this data for estimating g, the acceleration due to gravity. If the maximum percentage error in measurement of the distance and the time are e1 and e2respectively, then the maximum possible 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 Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A student measures the distance covered and time taken by a body under free fall which was intially at rest. He uses this data for estimating g, the acceleration due to gravity. If the maximum percentage error in measurement of the distance and the time are e1 and e2respectively, then the maximum possible 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?.
A student measures the distance covered and time taken by a body under free fall which was intially at rest. He uses this data for estimating g, the acceleration due to gravity. If the maximum percentage error in measurement of the distance and the time are e1 and e2respectively, then the maximum possible 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 Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about A student measures the distance covered and time taken by a body under free fall which was intially at rest. He uses this data for estimating g, the acceleration due to gravity. If the maximum percentage error in measurement of the distance and the time are e1 and e2respectively, then the maximum possible 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 Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A student measures the distance covered and time taken by a body under free fall which was intially at rest. He uses this data for estimating g, the acceleration due to gravity. If the maximum percentage error in measurement of the distance and the time are e1 and e2respectively, then the maximum possible 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 covered and time taken by a body under free fall which was intially at rest. He uses this data for estimating g, the acceleration due to gravity. If the maximum percentage error in measurement of the distance and the time are e1 and e2respectively, then the maximum possible 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?, a detailed solution for A student measures the distance covered and time taken by a body under free fall which was intially at rest. He uses this data for estimating g, the acceleration due to gravity. If the maximum percentage error in measurement of the distance and the time are e1 and e2respectively, then the maximum possible 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? has been provided alongside types of A student measures the distance covered and time taken by a body under free fall which was intially at rest. He uses this data for estimating g, the acceleration due to gravity. If the maximum percentage error in measurement of the distance and the time are e1 and e2respectively, then the maximum possible 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? theory, EduRev gives you an
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