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Determine the length of the copper wire which breaks under its own weight when suspended vertically from one end. Breaking stress for copper = 
and density of copper = 8600 
and density of copper = 8600 - a)2800 m
- b)2907 m
- c)3027 m
- d)none of these
Correct answer is option 'B'. Can you explain this answer?
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Given:
Breaking stress for copper = 2.45 × 10^8 N/m^2
Density of copper = 8600 kg/m^3
To find:
Length of copper wire which breaks under its own weight when suspended vertically from one end.
Solution:
Let us consider a small element of the wire of length ‘dx’ and radius ‘r’ at a distance ‘x’ from the lower end.
The weight of this element is given by:
dW = ρgdV
where ρ is the density of the wire, g is the acceleration due to gravity and dV is the volume of the element.
The volume of the element is given by:
dV = πr^2dx
The weight of the element can be written as:
dW = ρgπr^2dx
The stress on the wire is given by:
σ = F/A
where F is the force acting on the wire and A is the cross-sectional area of the wire.
The force acting on the wire is the weight of the wire itself, which is given by:
F = ρVg
where V is the volume of the wire.
The volume of the wire can be written as:
V = πr^2L
where L is the length of the wire.
Substituting V in the equation for F, we get:
F = ρπr^2gL
The cross-sectional area of the wire is given by:
A = πr^2
Substituting the values of F and A in the equation for stress, we get:
σ = ρgL
The wire will break when the stress in the wire is equal to the breaking stress of the wire.
Therefore, we have:
σ = σ_break
ρgL = σ_break
L = σ_break / (ρg)
Substituting the given values, we get:
L = 2.45 × 10^8 / (8600 × 9.8)
L = 2907 m
Therefore, the length of the copper wire which breaks under its own weight when suspended vertically from one end is 2907 m.
Hence, the correct option is (b).
Breaking stress for copper = 2.45 × 10^8 N/m^2
Density of copper = 8600 kg/m^3
To find:
Length of copper wire which breaks under its own weight when suspended vertically from one end.
Solution:
Let us consider a small element of the wire of length ‘dx’ and radius ‘r’ at a distance ‘x’ from the lower end.
The weight of this element is given by:
dW = ρgdV
where ρ is the density of the wire, g is the acceleration due to gravity and dV is the volume of the element.
The volume of the element is given by:
dV = πr^2dx
The weight of the element can be written as:
dW = ρgπr^2dx
The stress on the wire is given by:
σ = F/A
where F is the force acting on the wire and A is the cross-sectional area of the wire.
The force acting on the wire is the weight of the wire itself, which is given by:
F = ρVg
where V is the volume of the wire.
The volume of the wire can be written as:
V = πr^2L
where L is the length of the wire.
Substituting V in the equation for F, we get:
F = ρπr^2gL
The cross-sectional area of the wire is given by:
A = πr^2
Substituting the values of F and A in the equation for stress, we get:
σ = ρgL
The wire will break when the stress in the wire is equal to the breaking stress of the wire.
Therefore, we have:
σ = σ_break
ρgL = σ_break
L = σ_break / (ρg)
Substituting the given values, we get:
L = 2.45 × 10^8 / (8600 × 9.8)
L = 2907 m
Therefore, the length of the copper wire which breaks under its own weight when suspended vertically from one end is 2907 m.
Hence, the correct option is (b).
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Determine the length of the copper wire which breaks under its own weight when suspended vertically from one end. Breaking stress for copper = and density of copper = 8600 a)2800 m b)2907 mc) 3027 md) none of theseCorrect answer is option 'B'. Can you explain this answer?
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