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.
