The Young Modulus of the brass rod ≈ 8.5 × 10¹⁰ Pa or N/m².
<h3>How to find the young modulus of a brass rod?</h3>
Given: Physical Properties of the Brass rod exist
Length, L = 250 mm
Radius, R = Diameter / 2 = 25/2 mm
Load of 50 kN hanging on the brass rod which results in elongation of the rod to 0.3 mm.
To estimate the Young Modulus of the brass rod we will require Stress on the rod, Ratio of elongation to the total length.
To find the stress on the rod,
Stress(Pressure) = Force / Area
⇒ Stress = 50,000 / (Area of cross-section)
The rod exists shaped like a cylinder then the area of its cross-section will be πR² ( R = radius)
⇒ Stress = 50000 / (π (25/2 mm)² )
The force exists given in newton, then we must convert the unit of the area into m² to obtain the solution in pascal.
1 mm = 0.001 m
⇒ Stress = 50,000 / 22/7 ( 25/2 × 10⁻³ m)²
take, π = 22/7
⇒ Stress = 50000 / ( 22/7 × 625 / 4 × 10⁻⁶ )
⇒ Stress = 50000 / ( 11/14 × 625 × 10⁻6 )
⇒ Stress = 50000 × 14 × 10⁶ / 625×11
⇒ Stress = 80 × 14 × 10⁶ / 11
⇒ Stress = 1120/11 × 10⁶ Pa
Now, that we maintain Stressed, to estimate Strain (ratio of elongation to original length),
⇒ Strain = (Elongation) / (Original length)
⇒ Strain = 0.3 / 250
⇒ Strain = 3 / 2500
Therefore, Young Modulus, Y = Stress / Strain
⇒ Y = 1120/11 × 10⁶ / 3/2500
⇒ Y = 1120/11 × 2500/3 × 10⁶
⇒ Y = 101.8 × 833.3 × 10⁶
⇒ Y = 84829.94 × 10⁶
⇒ Y ≈ 8.5 × 10¹⁰ Pa
Therefore, the Young Modulus of the brass rod ≈ 8.5 × 10¹⁰ Pa or N/m².
To learn more about Young Modulus refer to:
brainly.com/question/13257353
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