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A load of 31.4kg is suspended from a wire of radius 0.001and density 9000 calculate the change in temperature of wire of 75% of workdone is converted to het will be the young modulus and specific heat capacity of material of the wire are 9.8 *ten to power ten and 490J/kg k ?
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A load of 31.4kg is suspended from a wire of radius 0.001and density 9...
Given:
- Load = 31.4 kg
- Radius of wire (r) = 0.001 m
- Density of wire (ρ) = 9000 kg/m³
- Young's modulus (E) = 9.8 x 10^10 N/m²
- Specific heat capacity (c) = 490 J/kg·K
To Find:
- Change in temperature of the wire when 75% of the work done is converted to heat.
Assumptions:
- The wire is uniform in composition and has a constant cross-sectional area.
- The wire is initially at a uniform temperature.
Explanation:
Step 1: Calculate the stress and strain on the wire:
The stress (σ) on the wire can be calculated using the formula:
σ = Load / Area
The area (A) of the wire can be calculated using the formula:
A = πr²
Substituting the given values:
A = π(0.001)² = 3.1415 x 10^-6 m²
σ = 31.4 / (3.1415 x 10^-6) = 9.9999 x 10^6 N/m²
The strain (ε) on the wire can be calculated using the formula:
ε = σ / E
Substituting the given values:
ε = (9.9999 x 10^6) / (9.8 x 10^10) = 1.0204 x 10^-4
Step 2: Calculate the work done:
The work done (W) on the wire can be calculated using the formula:
W = (1/2)σεV
where V is the volume of the wire.
The volume (V) of the wire can be calculated using the formula:
V = πr²h
where h is the height or length of the wire.
Assuming the wire is a cylinder:
V = π(0.001)²h
V = 3.1415 x 10^-6h
Substituting the given values:
W = (1/2)(9.9999 x 10^6)(1.0204 x 10^-4)(3.1415 x 10^-6h)
W = 1.6198 x 10^-3h
Step 3: Calculate the change in temperature:
Given that 75% of the work done is converted to heat, we can calculate the amount of heat (Q) generated using the formula:
Q = (75/100)W
Substituting the value of W calculated in Step 2:
Q = (75/100)(1.6198 x 10^-3h)
Q = 1.2148 x 10^-3h
The change in temperature (ΔT) of the wire can be calculated using the formula:
Q = mcΔT
where m is the mass of the wire, and c is the specific heat capacity.
The mass (m) of the wire can be calculated using the formula:
m = ρV
Substituting the value of V:
m = (9000)(3.1415 x 10^-6h)
m = 2.8274 x
- Load = 31.4 kg
- Radius of wire (r) = 0.001 m
- Density of wire (ρ) = 9000 kg/m³
- Young's modulus (E) = 9.8 x 10^10 N/m²
- Specific heat capacity (c) = 490 J/kg·K
To Find:
- Change in temperature of the wire when 75% of the work done is converted to heat.
Assumptions:
- The wire is uniform in composition and has a constant cross-sectional area.
- The wire is initially at a uniform temperature.
Explanation:
Step 1: Calculate the stress and strain on the wire:
The stress (σ) on the wire can be calculated using the formula:
σ = Load / Area
The area (A) of the wire can be calculated using the formula:
A = πr²
Substituting the given values:
A = π(0.001)² = 3.1415 x 10^-6 m²
σ = 31.4 / (3.1415 x 10^-6) = 9.9999 x 10^6 N/m²
The strain (ε) on the wire can be calculated using the formula:
ε = σ / E
Substituting the given values:
ε = (9.9999 x 10^6) / (9.8 x 10^10) = 1.0204 x 10^-4
Step 2: Calculate the work done:
The work done (W) on the wire can be calculated using the formula:
W = (1/2)σεV
where V is the volume of the wire.
The volume (V) of the wire can be calculated using the formula:
V = πr²h
where h is the height or length of the wire.
Assuming the wire is a cylinder:
V = π(0.001)²h
V = 3.1415 x 10^-6h
Substituting the given values:
W = (1/2)(9.9999 x 10^6)(1.0204 x 10^-4)(3.1415 x 10^-6h)
W = 1.6198 x 10^-3h
Step 3: Calculate the change in temperature:
Given that 75% of the work done is converted to heat, we can calculate the amount of heat (Q) generated using the formula:
Q = (75/100)W
Substituting the value of W calculated in Step 2:
Q = (75/100)(1.6198 x 10^-3h)
Q = 1.2148 x 10^-3h
The change in temperature (ΔT) of the wire can be calculated using the formula:
Q = mcΔT
where m is the mass of the wire, and c is the specific heat capacity.
The mass (m) of the wire can be calculated using the formula:
m = ρV
Substituting the value of V:
m = (9000)(3.1415 x 10^-6h)
m = 2.8274 x
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A load of 31.4kg is suspended from a wire of radius 0.001and density 9000 calculate the change in temperature of wire of 75% of workdone is converted to het will be the young modulus and specific heat capacity of material of the wire are 9.8 *ten to power ten and 490J/kg k ?
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A load of 31.4kg is suspended from a wire of radius 0.001and density 9000 calculate the change in temperature of wire of 75% of workdone is converted to het will be the young modulus and specific heat capacity of material of the wire are 9.8 *ten to power ten and 490J/kg k ? 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 0.001and density 9000 calculate the change in temperature of wire of 75% of workdone is converted to het will be the young modulus and specific heat capacity of material of the wire are 9.8 *ten to power ten and 490J/kg k ? 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 0.001and density 9000 calculate the change in temperature of wire of 75% of workdone is converted to het will be the young modulus and specific heat capacity of material of the wire are 9.8 *ten to power ten and 490J/kg k ?.
A load of 31.4kg is suspended from a wire of radius 0.001and density 9000 calculate the change in temperature of wire of 75% of workdone is converted to het will be the young modulus and specific heat capacity of material of the wire are 9.8 *ten to power ten and 490J/kg k ? 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 0.001and density 9000 calculate the change in temperature of wire of 75% of workdone is converted to het will be the young modulus and specific heat capacity of material of the wire are 9.8 *ten to power ten and 490J/kg k ? 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 0.001and density 9000 calculate the change in temperature of wire of 75% of workdone is converted to het will be the young modulus and specific heat capacity of material of the wire are 9.8 *ten to power ten and 490J/kg k ?.
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