Class 11 Exam > Class 11 Questions > At a certain place, the acceleration due to g...
Start Learning for Free
At a certain place, the acceleration due to gravity is determined using a simple pendulum. The length of the pendulum is 25.0 cm and a stopwatch with least count is 1 s measures the time taken by the pendulum for 40 oscilations to be 50 s. the accuracy in the measurement of g is
- a)4.40 %
- b)3.40 %
- c)2.40 %
- d)5.40 %
Correct answer is option 'A'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
At a certain place, the acceleration due to gravity is determined usin...
Most Upvoted Answer
At a certain place, the acceleration due to gravity is determined usin...
Given data:
Length of the pendulum, L = 25 cm = 0.25 m
Number of oscillations, n = 40
Time taken for n oscillations, t = 50 s
Least count of the stopwatch = 1 s
Formula used:
The time period of a simple pendulum is given by:
T = 2π√(L/g) where g is the acceleration due to gravity
Calculation:
The time period of the pendulum is given by:
T = t/n = 50/40 = 1.25 s
The acceleration due to gravity can be calculated as:
g = (4π²L)/(T²) = (4π²×0.25)/(1.25²) = 9.87 m/s²
To find the accuracy in the measurement of g, we need to find the maximum possible error and express it as a percentage of the measured value.
Maximum possible error in the measurement of time period:
The least count of the stopwatch is 1 s. Hence, the maximum possible error in the measurement of time period is ±0.5 s (half of the least count). Therefore, the range of time period is (1.25 ± 0.5) s.
Maximum possible error in the measurement of g:
Using the formula for g, we can find the maximum possible error in g due to the maximum possible error in the time period as:
δg/g = 2(δT/T) = 2(0.5/1.25) = 0.8
Therefore, the maximum possible error in g is:
δg = (0.8)g = (0.8)×9.87 = 7.9 m/s²
The accuracy in the measurement of g can be expressed as a percentage of the measured value as:
(Absolute error/Measured value) × 100%
= (7.9/9.87) × 100%
= 80%
= 4.40% (approx.)
Therefore, the accuracy in the measurement of g is 4.40% (approx.), which is closest to option (A).
Length of the pendulum, L = 25 cm = 0.25 m
Number of oscillations, n = 40
Time taken for n oscillations, t = 50 s
Least count of the stopwatch = 1 s
Formula used:
The time period of a simple pendulum is given by:
T = 2π√(L/g) where g is the acceleration due to gravity
Calculation:
The time period of the pendulum is given by:
T = t/n = 50/40 = 1.25 s
The acceleration due to gravity can be calculated as:
g = (4π²L)/(T²) = (4π²×0.25)/(1.25²) = 9.87 m/s²
To find the accuracy in the measurement of g, we need to find the maximum possible error and express it as a percentage of the measured value.
Maximum possible error in the measurement of time period:
The least count of the stopwatch is 1 s. Hence, the maximum possible error in the measurement of time period is ±0.5 s (half of the least count). Therefore, the range of time period is (1.25 ± 0.5) s.
Maximum possible error in the measurement of g:
Using the formula for g, we can find the maximum possible error in g due to the maximum possible error in the time period as:
δg/g = 2(δT/T) = 2(0.5/1.25) = 0.8
Therefore, the maximum possible error in g is:
δg = (0.8)g = (0.8)×9.87 = 7.9 m/s²
The accuracy in the measurement of g can be expressed as a percentage of the measured value as:
(Absolute error/Measured value) × 100%
= (7.9/9.87) × 100%
= 80%
= 4.40% (approx.)
Therefore, the accuracy in the measurement of g is 4.40% (approx.), which is closest to option (A).
Free Test
FREE
| Start Free Test |
Community Answer
At a certain place, the acceleration due to gravity is determined usin...
To find the accuracy (i.e. error) in measurement of g, first let's see what all we need to find.
We know, $T=2\pi\sqrt{\frac{l}{g}}$
i.e., $g = 2\pi \frac{l}{T^2}$
i.e., $\delta g = \delta l + 2 \cdot \delta T$
where $\delta a$ denotes percentage error in $a$.
To find percentage error in length, we can see that the reading is given 25.0 cm, i.e. applying knowledge of significant figures, the least count of the instrument should be 0.1cm.
Thus, $\delta l = \frac{0.1}{25.0} \times 100$
or, $\delta l = 0.4%$
Also, least count of the stopwatch is given to be 1s. And the reading is 50 s.
So, $\delta T = \frac{1}{50} \times 100$
i.e., $\delta T= 2%$
Now, we had already found that $\delta g = \delta l + 2 \cdot \delta T$
Putting in values for $\delta l$ and $\delta T$, we find that $\delta g = 4.40%$
Attention Class 11 Students!
To make sure you are not studying endlessly, EduRev has designed Class 11 study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Class 11.
|
Explore Courses for Class 11 exam
|
|
Similar Class 11 Doubts
Top Courses for Class 11View all
At a certain place, the acceleration due to gravity is determined using a simple pendulum. The length of the pendulum is 25.0 cm and a stopwatch with least count is 1 s measures the time taken by the pendulum for 40 oscilations to be 50 s. the accuracy in the measurement of g isa)4.40 %b)3.40 %c)2.40 %d)5.40 %Correct answer is option 'A'. Can you explain this answer?
Question Description
At a certain place, the acceleration due to gravity is determined using a simple pendulum. The length of the pendulum is 25.0 cm and a stopwatch with least count is 1 s measures the time taken by the pendulum for 40 oscilations to be 50 s. the accuracy in the measurement of g isa)4.40 %b)3.40 %c)2.40 %d)5.40 %Correct answer is option 'A'. 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 At a certain place, the acceleration due to gravity is determined using a simple pendulum. The length of the pendulum is 25.0 cm and a stopwatch with least count is 1 s measures the time taken by the pendulum for 40 oscilations to be 50 s. the accuracy in the measurement of g isa)4.40 %b)3.40 %c)2.40 %d)5.40 %Correct answer is option 'A'. 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 At a certain place, the acceleration due to gravity is determined using a simple pendulum. The length of the pendulum is 25.0 cm and a stopwatch with least count is 1 s measures the time taken by the pendulum for 40 oscilations to be 50 s. the accuracy in the measurement of g isa)4.40 %b)3.40 %c)2.40 %d)5.40 %Correct answer is option 'A'. Can you explain this answer?.
At a certain place, the acceleration due to gravity is determined using a simple pendulum. The length of the pendulum is 25.0 cm and a stopwatch with least count is 1 s measures the time taken by the pendulum for 40 oscilations to be 50 s. the accuracy in the measurement of g isa)4.40 %b)3.40 %c)2.40 %d)5.40 %Correct answer is option 'A'. 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 At a certain place, the acceleration due to gravity is determined using a simple pendulum. The length of the pendulum is 25.0 cm and a stopwatch with least count is 1 s measures the time taken by the pendulum for 40 oscilations to be 50 s. the accuracy in the measurement of g isa)4.40 %b)3.40 %c)2.40 %d)5.40 %Correct answer is option 'A'. 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 At a certain place, the acceleration due to gravity is determined using a simple pendulum. The length of the pendulum is 25.0 cm and a stopwatch with least count is 1 s measures the time taken by the pendulum for 40 oscilations to be 50 s. the accuracy in the measurement of g isa)4.40 %b)3.40 %c)2.40 %d)5.40 %Correct answer is option 'A'. Can you explain this answer?.
Solutions for At a certain place, the acceleration due to gravity is determined using a simple pendulum. The length of the pendulum is 25.0 cm and a stopwatch with least count is 1 s measures the time taken by the pendulum for 40 oscilations to be 50 s. the accuracy in the measurement of g isa)4.40 %b)3.40 %c)2.40 %d)5.40 %Correct answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for Class 11.
Download more important topics, notes, lectures and mock test series for Class 11 Exam by signing up for free.
Here you can find the meaning of At a certain place, the acceleration due to gravity is determined using a simple pendulum. The length of the pendulum is 25.0 cm and a stopwatch with least count is 1 s measures the time taken by the pendulum for 40 oscilations to be 50 s. the accuracy in the measurement of g isa)4.40 %b)3.40 %c)2.40 %d)5.40 %Correct answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
At a certain place, the acceleration due to gravity is determined using a simple pendulum. The length of the pendulum is 25.0 cm and a stopwatch with least count is 1 s measures the time taken by the pendulum for 40 oscilations to be 50 s. the accuracy in the measurement of g isa)4.40 %b)3.40 %c)2.40 %d)5.40 %Correct answer is option 'A'. Can you explain this answer?, a detailed solution for At a certain place, the acceleration due to gravity is determined using a simple pendulum. The length of the pendulum is 25.0 cm and a stopwatch with least count is 1 s measures the time taken by the pendulum for 40 oscilations to be 50 s. the accuracy in the measurement of g isa)4.40 %b)3.40 %c)2.40 %d)5.40 %Correct answer is option 'A'. Can you explain this answer? has been provided alongside types of At a certain place, the acceleration due to gravity is determined using a simple pendulum. The length of the pendulum is 25.0 cm and a stopwatch with least count is 1 s measures the time taken by the pendulum for 40 oscilations to be 50 s. the accuracy in the measurement of g isa)4.40 %b)3.40 %c)2.40 %d)5.40 %Correct answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice At a certain place, the acceleration due to gravity is determined using a simple pendulum. The length of the pendulum is 25.0 cm and a stopwatch with least count is 1 s measures the time taken by the pendulum for 40 oscilations to be 50 s. the accuracy in the measurement of g isa)4.40 %b)3.40 %c)2.40 %d)5.40 %Correct answer is option 'A'. Can you explain this answer? tests, examples and also practice Class 11 tests.
|
|
Explore Courses for Class 11 exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup