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Two wires with equal lengths are made of pure copper. The diameter of wire A is three times the diameter of wire B. When 8 kg masses are hung on the wires, wire B stretches more than wire A. You make careful measurements and compute Young's modulus for both wires. What do you find?a. YA > YBb. YA = YBc. YA < YB

Respuesta :

Answer: c. YA < YB

Explanation:

The formula for Young’s modulus is = Tensile stress / Tensile strain

Tensile stress = Force x Length

Force = mass x acceleration due to gravity

 = 8kg x 10m/s

 = 80kgm/s

Tensile stress  = 80kgm/s x 2m = 160kgm2/s

Tensile strain = Area x change in length

Area = pi x D2 / 4 ; Pi = 3.14

Change in length = L2 – L1 (New length – Initial length)

Given parameters:

Length of wire A = Length of wire B, (let’s use 2meters for the calculation)

For wire A, Diameter = 3 x Wire B diameter

Assuming Diameter of wire B = 1meter

Therefore, diameter of wire A = 1 x 3 = 3meters

It is said that wire B stretches more than wire A when the man of 8kg is placed on both

For wire B, let’s assume new length is = 4m

For wire A let’s assume new length is = 3m.

(i) Tensile strain of wire A =  

Area of wire A = 3.14 x (32)/4 = 7.065m2

Change in length = 3m - 2m = 1m.

Therefore, tensile strain = 7.065m2 x 1m = 7.065m3

Young’s modulus for wire A (YA) = 160kgm2/s divided by 7.065m3  

   = 22.64Pa.

(ii) Tensile strain of wire B =

Area of wire B = 3.14 x (12)/4 = 0.785m2

Change in length = 4m – 2m = 2m

Therefore, tensile strain = 0.785m2 x 2m = 1.57m3

Young’s modulus for wire B (YB) = 160kgm2/s divided by 1.57m3

   = 101.91Pa.

From the calculations above, we see that YA is less than YB (YA < YB). This is true given that wire A has a greater diameter than wire B which in turn impacts the Area of the wire since the diameter is directly proportional to area and the area is inversely proportional to the young’s modulus.

Cricetus

"[tex]Y_A = Y_B[/tex]" would be the correct solution.

Young's modulus:

Young's modulus seems to be a materials and substances characteristic that varies with temperatures. It is determined by the nature of the material and is unaffected by form or breadth.

it is always defined as that of the stress-to-strain ratio.

Thus we can say that the Young's modulus for both wires would be equivalent.

Hence, the above answer that is "[tex]Y_A =Y_B[/tex]" is correct.

Find out more information about Young's modulus here:

https://brainly.com/question/6864866

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