GATE Exam > GATE Questions > The radius of a sphere is given as (40.0 ± 0...
Start Learning for Free
The radius of a sphere is given as (40.0 ± 0.5) mm. The estimated error in its mass is: (2002)
- a)±3.75%
- b)± 1.25%
- c)± 12.5%
- d)± 0/125%
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
The radius of a sphere is given as (40.0 ± 0.5) mm. The estimated err...
Estimated error
View all questions of this test
Most Upvoted Answer
The radius of a sphere is given as (40.0 ± 0.5) mm. The estimated err...
Estimated error
Free Test
FREE
| Start Free Test |
Community Answer
The radius of a sphere is given as (40.0 ± 0.5) mm. The estimated err...
Calculation of estimated error in mass
- The volume of a sphere is given by V = (4/3)πr^3, where r is the radius of the sphere.
- The mass of the sphere is directly proportional to its volume.
- Therefore, the error in mass can be calculated using the error propagation formula: δm/m = 3δr/r, where δm is the error in mass, δr is the error in radius, and r is the radius of the sphere.
Given data
- Radius (r) = 40.0 mm
- Error in radius (δr) = 0.5 mm
Calculation
- δm/m = 3(0.5/40.0) = 0.075
- This implies that the estimated error in mass is ±7.5% of the actual mass.
- However, since the options are presented in terms of ±x%, we convert 7.5% to 1.25% (1% = 0.01) to match the closest option.
Therefore, the correct answer is option 'B' ±1.25%.
- The volume of a sphere is given by V = (4/3)πr^3, where r is the radius of the sphere.
- The mass of the sphere is directly proportional to its volume.
- Therefore, the error in mass can be calculated using the error propagation formula: δm/m = 3δr/r, where δm is the error in mass, δr is the error in radius, and r is the radius of the sphere.
Given data
- Radius (r) = 40.0 mm
- Error in radius (δr) = 0.5 mm
Calculation
- δm/m = 3(0.5/40.0) = 0.075
- This implies that the estimated error in mass is ±7.5% of the actual mass.
- However, since the options are presented in terms of ±x%, we convert 7.5% to 1.25% (1% = 0.01) to match the closest option.
Therefore, the correct answer is option 'B' ±1.25%.
|
Explore Courses for GATE exam
|
|
Top Courses for GATEView all
Question Description
The radius of a sphere is given as (40.0 ± 0.5) mm. The estimated error in its mass is: (2002)a)±3.75%b)± 1.25%c)± 12.5%d)± 0/125%Correct answer is option 'B'. Can you explain this answer? for GATE 2025 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about The radius of a sphere is given as (40.0 ± 0.5) mm. The estimated error in its mass is: (2002)a)±3.75%b)± 1.25%c)± 12.5%d)± 0/125%Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for GATE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The radius of a sphere is given as (40.0 ± 0.5) mm. The estimated error in its mass is: (2002)a)±3.75%b)± 1.25%c)± 12.5%d)± 0/125%Correct answer is option 'B'. Can you explain this answer?.
The radius of a sphere is given as (40.0 ± 0.5) mm. The estimated error in its mass is: (2002)a)±3.75%b)± 1.25%c)± 12.5%d)± 0/125%Correct answer is option 'B'. Can you explain this answer? for GATE 2025 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about The radius of a sphere is given as (40.0 ± 0.5) mm. The estimated error in its mass is: (2002)a)±3.75%b)± 1.25%c)± 12.5%d)± 0/125%Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for GATE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The radius of a sphere is given as (40.0 ± 0.5) mm. The estimated error in its mass is: (2002)a)±3.75%b)± 1.25%c)± 12.5%d)± 0/125%Correct answer is option 'B'. Can you explain this answer?.
Solutions for The radius of a sphere is given as (40.0 ± 0.5) mm. The estimated error in its mass is: (2002)a)±3.75%b)± 1.25%c)± 12.5%d)± 0/125%Correct answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for GATE.
Download more important topics, notes, lectures and mock test series for GATE Exam by signing up for free.
Here you can find the meaning of The radius of a sphere is given as (40.0 ± 0.5) mm. The estimated error in its mass is: (2002)a)±3.75%b)± 1.25%c)± 12.5%d)± 0/125%Correct answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
The radius of a sphere is given as (40.0 ± 0.5) mm. The estimated error in its mass is: (2002)a)±3.75%b)± 1.25%c)± 12.5%d)± 0/125%Correct answer is option 'B'. Can you explain this answer?, a detailed solution for The radius of a sphere is given as (40.0 ± 0.5) mm. The estimated error in its mass is: (2002)a)±3.75%b)± 1.25%c)± 12.5%d)± 0/125%Correct answer is option 'B'. Can you explain this answer? has been provided alongside types of The radius of a sphere is given as (40.0 ± 0.5) mm. The estimated error in its mass is: (2002)a)±3.75%b)± 1.25%c)± 12.5%d)± 0/125%Correct answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice The radius of a sphere is given as (40.0 ± 0.5) mm. The estimated error in its mass is: (2002)a)±3.75%b)± 1.25%c)± 12.5%d)± 0/125%Correct answer is option 'B'. Can you explain this answer? tests, examples and also practice GATE tests.
|
|
Explore Courses for GATE exam
|
|
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 on EduRev and stay on top of your study goals
10M+ students crushing their study goals daily