JEE Exam > JEE Questions > A load of 31.4kg is suspended from a wire of ...
Start Learning for Free
A load of 31.4kg is suspended from a wire of radius 10^-3m and density 9×10^3kg/m^3 . Calculate the Change in temp. Of wire if 75%of the work done is converted into heat will be :( young modules and specific heat capacity of the material of the wire are 9.8×10^10N/m^2 and 490 J/Kgk , respectively)?
Most Upvoted Answer
A load of 31.4kg is suspended from a wire of radius 10^-3m and density...
Problem:
Calculate the change in temperature of a wire if a load of 31.4kg is suspended from a wire of radius 10^-3m and density 9×10^3kg/m^3. Young's modulus and specific heat capacity of the material of the wire are 9.8×10^10N/m^2 and 490 J/KgK, respectively, and 75% of the work done is converted into heat.
Solution:
Step 1: Calculate the stress and strain in the wire
The stress in the wire can be calculated using the formula:
Stress = Force/Area = mg/Area
where m = the mass of the load, and g = acceleration due to gravity (9.8 m/s^2)
m = 31.4 kg
g = 9.8 m/s^2
Area = πr^2 = π(10^-3)^2 = 3.14×10^-6 m^2
Stress = mg/Area = 31.4×9.8/3.14×10^-6 = 9.75×10^7 N/m^2
The strain in the wire can be calculated using the formula:
Strain = Stress/Young's modulus
Strain = 9.75×10^7/9.8×10^10 = 9.95×10^-4
Step 2: Calculate the work done
The work done can be calculated using the formula:
Work = Force x Displacement
Displacement = Strain x Length
Length = 2πr = 2π(10^-3) = 6.28×10^-3 m
Displacement = Strain x Length = 9.95×10^-4 × 6.28×10^-3 = 6.25×10^-6 m
Force = mg = 31.4×9.8 = 307.72 N
Work = Force x Displacement = 307.72 × 6.25×10^-6 = 1.92×10^-3 J
Step 3: Calculate the heat produced
75% of the work done is converted into heat, so
Heat produced = 75/100 × 1.92×10^-3 = 1.44×10^-3 J
Step 4: Calculate the change in temperature
The mass of the wire can be calculated using the formula:
Mass = Volume x Density
Volume = πr^2h
Assuming the wire is a cylinder, the height can be taken as the length of the wire:
h = Length = 6.28×10^-3 m
Volume = π(10^-3)^2 × 6.28×10^-3 = 1.98×10^-8 m^3
Mass = Volume x Density = 1.98×10^-8 × 9×10^3 = 0.1782×10^-4 kg
The heat produced is used to increase the temperature of the wire:
Heat produced = Mass x Specific
Calculate the change in temperature of a wire if a load of 31.4kg is suspended from a wire of radius 10^-3m and density 9×10^3kg/m^3. Young's modulus and specific heat capacity of the material of the wire are 9.8×10^10N/m^2 and 490 J/KgK, respectively, and 75% of the work done is converted into heat.
Solution:
Step 1: Calculate the stress and strain in the wire
The stress in the wire can be calculated using the formula:
Stress = Force/Area = mg/Area
where m = the mass of the load, and g = acceleration due to gravity (9.8 m/s^2)
m = 31.4 kg
g = 9.8 m/s^2
Area = πr^2 = π(10^-3)^2 = 3.14×10^-6 m^2
Stress = mg/Area = 31.4×9.8/3.14×10^-6 = 9.75×10^7 N/m^2
The strain in the wire can be calculated using the formula:
Strain = Stress/Young's modulus
Strain = 9.75×10^7/9.8×10^10 = 9.95×10^-4
Step 2: Calculate the work done
The work done can be calculated using the formula:
Work = Force x Displacement
Displacement = Strain x Length
Length = 2πr = 2π(10^-3) = 6.28×10^-3 m
Displacement = Strain x Length = 9.95×10^-4 × 6.28×10^-3 = 6.25×10^-6 m
Force = mg = 31.4×9.8 = 307.72 N
Work = Force x Displacement = 307.72 × 6.25×10^-6 = 1.92×10^-3 J
Step 3: Calculate the heat produced
75% of the work done is converted into heat, so
Heat produced = 75/100 × 1.92×10^-3 = 1.44×10^-3 J
Step 4: Calculate the change in temperature
The mass of the wire can be calculated using the formula:
Mass = Volume x Density
Volume = πr^2h
Assuming the wire is a cylinder, the height can be taken as the length of the wire:
h = Length = 6.28×10^-3 m
Volume = π(10^-3)^2 × 6.28×10^-3 = 1.98×10^-8 m^3
Mass = Volume x Density = 1.98×10^-8 × 9×10^3 = 0.1782×10^-4 kg
The heat produced is used to increase the temperature of the wire:
Heat produced = Mass x Specific
Community Answer
A load of 31.4kg is suspended from a wire of radius 10^-3m and density...
Please solve this question...
Attention JEE Students!
To make sure you are not studying endlessly, EduRev has designed JEE study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in JEE.
|
Explore Courses for JEE exam
|
|
Similar JEE Doubts
Top Courses for JEEView all
A load of 31.4kg is suspended from a wire of radius 10^-3m and density 9×10^3kg/m^3 . Calculate the Change in temp. Of wire if 75%of the work done is converted into heat will be :( young modules and specific heat capacity of the material of the wire are 9.8×10^10N/m^2 and 490 J/Kgk , respectively)?
Question Description
A load of 31.4kg is suspended from a wire of radius 10^-3m and density 9×10^3kg/m^3 . Calculate the Change in temp. Of wire if 75%of the work done is converted into heat will be :( young modules and specific heat capacity of the material of the wire are 9.8×10^10N/m^2 and 490 J/Kgk , respectively)? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A load of 31.4kg is suspended from a wire of radius 10^-3m and density 9×10^3kg/m^3 . Calculate the Change in temp. Of wire if 75%of the work done is converted into heat will be :( young modules and specific heat capacity of the material of the wire are 9.8×10^10N/m^2 and 490 J/Kgk , respectively)? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A load of 31.4kg is suspended from a wire of radius 10^-3m and density 9×10^3kg/m^3 . Calculate the Change in temp. Of wire if 75%of the work done is converted into heat will be :( young modules and specific heat capacity of the material of the wire are 9.8×10^10N/m^2 and 490 J/Kgk , respectively)?.
A load of 31.4kg is suspended from a wire of radius 10^-3m and density 9×10^3kg/m^3 . Calculate the Change in temp. Of wire if 75%of the work done is converted into heat will be :( young modules and specific heat capacity of the material of the wire are 9.8×10^10N/m^2 and 490 J/Kgk , respectively)? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A load of 31.4kg is suspended from a wire of radius 10^-3m and density 9×10^3kg/m^3 . Calculate the Change in temp. Of wire if 75%of the work done is converted into heat will be :( young modules and specific heat capacity of the material of the wire are 9.8×10^10N/m^2 and 490 J/Kgk , respectively)? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A load of 31.4kg is suspended from a wire of radius 10^-3m and density 9×10^3kg/m^3 . Calculate the Change in temp. Of wire if 75%of the work done is converted into heat will be :( young modules and specific heat capacity of the material of the wire are 9.8×10^10N/m^2 and 490 J/Kgk , respectively)?.
Solutions for A load of 31.4kg is suspended from a wire of radius 10^-3m and density 9×10^3kg/m^3 . Calculate the Change in temp. Of wire if 75%of the work done is converted into heat will be :( young modules and specific heat capacity of the material of the wire are 9.8×10^10N/m^2 and 490 J/Kgk , respectively)? in English & in Hindi are available as part of our courses for JEE.
Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free.
Here you can find the meaning of A load of 31.4kg is suspended from a wire of radius 10^-3m and density 9×10^3kg/m^3 . Calculate the Change in temp. Of wire if 75%of the work done is converted into heat will be :( young modules and specific heat capacity of the material of the wire are 9.8×10^10N/m^2 and 490 J/Kgk , respectively)? defined & explained in the simplest way possible. Besides giving the explanation of
A load of 31.4kg is suspended from a wire of radius 10^-3m and density 9×10^3kg/m^3 . Calculate the Change in temp. Of wire if 75%of the work done is converted into heat will be :( young modules and specific heat capacity of the material of the wire are 9.8×10^10N/m^2 and 490 J/Kgk , respectively)?, a detailed solution for A load of 31.4kg is suspended from a wire of radius 10^-3m and density 9×10^3kg/m^3 . Calculate the Change in temp. Of wire if 75%of the work done is converted into heat will be :( young modules and specific heat capacity of the material of the wire are 9.8×10^10N/m^2 and 490 J/Kgk , respectively)? has been provided alongside types of A load of 31.4kg is suspended from a wire of radius 10^-3m and density 9×10^3kg/m^3 . Calculate the Change in temp. Of wire if 75%of the work done is converted into heat will be :( young modules and specific heat capacity of the material of the wire are 9.8×10^10N/m^2 and 490 J/Kgk , respectively)? theory, EduRev gives you an
ample number of questions to practice A load of 31.4kg is suspended from a wire of radius 10^-3m and density 9×10^3kg/m^3 . Calculate the Change in temp. Of wire if 75%of the work done is converted into heat will be :( young modules and specific heat capacity of the material of the wire are 9.8×10^10N/m^2 and 490 J/Kgk , respectively)? tests, examples and also practice JEE tests.
|
|
Explore Courses for JEE 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
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup