A steel rod has a radius of 10 mm and a length of 1.0 m. A force stretches it along its length and produce a strain of 0.16%. Young’s modulus of the steel is 2.0 x 10¹¹ Nm⁻². What is the magnitude of the force stretching the rod?
Magnitude refers to the size or quantity of a physical property often expressed in numerical terms. It can apply to various measurements such as force mass or energy. Understanding magnitude is essential in physics and engineering as it helps quantify relationships between different physical quantities and assess the impact of forces and interactions.
Class 11 Physics Chapter 8 discusses mechanical properties of solids including stress strain relationships Young’s modulus bulk modulus and shear modulus. It covers elasticity Hooke’s law factors affecting elasticity and their practical applications. These topics are essential for understanding material behavior and designing reliable structures in engineering and construction.
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The expression of stress, strain, and Young’s modulus is as follows:
Stress = Y × Strain
where,
– Y = 2.0 × 10¹¹ N/m²
– Strain = 0.16% = 0.0016
Stress can also be defined as follows:
Stress = Force / Area
Cross-sectional area of the rod
A = πr² = π × (10 × 10⁻³)² = π × 10⁻⁴ m²
Put it into the equation for stress:
Y × Strain = Force / Area
Force =
Force = Y × Strain × A
Put the values:
Force = (2.0 × 10¹¹) × (0.0016) × (π × 10⁻⁴)
Force = 100.5 × 10³ N ≈ 100 kN
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