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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)?
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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
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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)?
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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)?.
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