NEET Exam > NEET Questions > A circular steel wire 2.00 m long must stretc...
Start Learning for Free
A circular steel wire 2.00 m long must stretch no more than 0.25 m when a tensile force of 400N is applied to each of the wire what minimum diameter is required of the wire?
Verified Answer
A circular steel wire 2.00 m long must stretch no more than 0.25 m whe...
This question is part of UPSC exam. View all NEET courses
Most Upvoted Answer
A circular steel wire 2.00 m long must stretch no more than 0.25 m whe...
Given data:
- Length of the wire (L) = 2.00 m
- Maximum stretch (ΔL) = 0.25 m
- Tensile force (F) = 400 N
Formula:
The formula to calculate the stretch in a wire under tensile force is:
\[ \Delta L = \frac{FL}{A \cdot Y} \]
where,
ΔL = stretch in the wire,
F = tensile force,
L = original length of the wire,
A = cross-sectional area of the wire, and
Y = Young's modulus of the material
Finding the minimum diameter:
- Since the wire is circular, the cross-sectional area can be calculated as:
\[ A = \frac{\pi d^2}{4} \]
where,
d = diameter of the wire
- Substituting the values in the formula, we get:
\[ 0.25 = \frac{400 \cdot 2}{\frac{\pi d^2}{4} \cdot Y} \]
\[ 0.25 = \frac{800}{\pi d^2 \cdot Y} \]
\[ d^2 = \frac{800}{0.25 \cdot \pi \cdot Y} \]
\[ d^2 = \frac{800}{0.25 \cdot 3.14 \cdot Y} \]
\[ d^2 = \frac{800}{0.785 \cdot Y} \]
\[ d^2 = \frac{800}{Y} \]
\[ d = \sqrt{\frac{800}{Y}} \]
Conclusion:
To ensure that the wire does not stretch more than 0.25 m when a tensile force of 400 N is applied, the minimum diameter required for the wire can be calculated using the formula above.
- Length of the wire (L) = 2.00 m
- Maximum stretch (ΔL) = 0.25 m
- Tensile force (F) = 400 N
Formula:
The formula to calculate the stretch in a wire under tensile force is:
\[ \Delta L = \frac{FL}{A \cdot Y} \]
where,
ΔL = stretch in the wire,
F = tensile force,
L = original length of the wire,
A = cross-sectional area of the wire, and
Y = Young's modulus of the material
Finding the minimum diameter:
- Since the wire is circular, the cross-sectional area can be calculated as:
\[ A = \frac{\pi d^2}{4} \]
where,
d = diameter of the wire
- Substituting the values in the formula, we get:
\[ 0.25 = \frac{400 \cdot 2}{\frac{\pi d^2}{4} \cdot Y} \]
\[ 0.25 = \frac{800}{\pi d^2 \cdot Y} \]
\[ d^2 = \frac{800}{0.25 \cdot \pi \cdot Y} \]
\[ d^2 = \frac{800}{0.25 \cdot 3.14 \cdot Y} \]
\[ d^2 = \frac{800}{0.785 \cdot Y} \]
\[ d^2 = \frac{800}{Y} \]
\[ d = \sqrt{\frac{800}{Y}} \]
Conclusion:
To ensure that the wire does not stretch more than 0.25 m when a tensile force of 400 N is applied, the minimum diameter required for the wire can be calculated using the formula above.
Attention NEET Students!
To make sure you are not studying endlessly, EduRev has designed NEET study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in NEET.
|
|
Explore Courses for NEET exam
|
|
Similar NEET Doubts
Top Courses for NEETView all
A circular steel wire 2.00 m long must stretch no more than 0.25 m when a tensile force of 400N is applied to each of the wire what minimum diameter is required of the wire?
Question Description
A circular steel wire 2.00 m long must stretch no more than 0.25 m when a tensile force of 400N is applied to each of the wire what minimum diameter is required of the wire? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A circular steel wire 2.00 m long must stretch no more than 0.25 m when a tensile force of 400N is applied to each of the wire what minimum diameter is required of the wire? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A circular steel wire 2.00 m long must stretch no more than 0.25 m when a tensile force of 400N is applied to each of the wire what minimum diameter is required of the wire?.
A circular steel wire 2.00 m long must stretch no more than 0.25 m when a tensile force of 400N is applied to each of the wire what minimum diameter is required of the wire? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A circular steel wire 2.00 m long must stretch no more than 0.25 m when a tensile force of 400N is applied to each of the wire what minimum diameter is required of the wire? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A circular steel wire 2.00 m long must stretch no more than 0.25 m when a tensile force of 400N is applied to each of the wire what minimum diameter is required of the wire?.
Solutions for A circular steel wire 2.00 m long must stretch no more than 0.25 m when a tensile force of 400N is applied to each of the wire what minimum diameter is required of the wire? in English & in Hindi are available as part of our courses for NEET.
Download more important topics, notes, lectures and mock test series for NEET Exam by signing up for free.
Here you can find the meaning of A circular steel wire 2.00 m long must stretch no more than 0.25 m when a tensile force of 400N is applied to each of the wire what minimum diameter is required of the wire? defined & explained in the simplest way possible. Besides giving the explanation of
A circular steel wire 2.00 m long must stretch no more than 0.25 m when a tensile force of 400N is applied to each of the wire what minimum diameter is required of the wire?, a detailed solution for A circular steel wire 2.00 m long must stretch no more than 0.25 m when a tensile force of 400N is applied to each of the wire what minimum diameter is required of the wire? has been provided alongside types of A circular steel wire 2.00 m long must stretch no more than 0.25 m when a tensile force of 400N is applied to each of the wire what minimum diameter is required of the wire? theory, EduRev gives you an
ample number of questions to practice A circular steel wire 2.00 m long must stretch no more than 0.25 m when a tensile force of 400N is applied to each of the wire what minimum diameter is required of the wire? tests, examples and also practice NEET tests.
|
|
Explore Courses for NEET 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