A steel rod has a radius of 10 mm and length of 1 m. A 100 kN force F stretches it along its length. Calculate (a) stress, (b) elongation and (c) strain on the rod, given Young's modulus of steel = 2 x 10^11 N/m^2.

**OR**

The average depth of the Indian Ocean is about 3000 m. C

Question

A steel rod has a radius of 10 mm and length of 1 m. A 100 kN force F stretches it along its length. Calculate (a) stress, (b) elongation and (c) strain on the rod, given Young's modulus of steel = 2 x 10^11 N/m^2.

**OR**

The average depth of the Indian Ocean is about 3000 m. Calculate the fractional compression (delta V / V) of water at the bottom of the ocean, given that the bulk modulus of water is 2.2 x 10^9 N/m^2. (Take g = 10 m/s^2)

Accepted Answer

>

> [!TLDR]
> For the steel rod: stress ≈ 3.18×10⁸ N/m², elongation ≈ 1.59 mm, strain ≈ 1.59×10⁻³.
>
> Given: radius r = 10 mm = 1.0 × 10⁻² m, length L = 1 m, force F = 100 kN = 1.0 × 10⁵ N, Young's modulus Y = 2 × 10¹¹ N/m².
>
> Step 1 — Cross-sectional area:
> A = πr² = π × (1.0×10⁻²)² = π × 1.0×10⁻⁴ ≈ 3.1416 × 10⁻⁴ m²
>
> Step 2 — (a) Stress:
> Stress = F/A = (1.0×10⁵) / (3.1416×10⁻⁴) ≈ 3.183 × 10⁸ N/m²
>
> Step 3 — (c) Strain (from the definition of Young's modulus, Y = stress/strain): …

Q.A steel rod has a radius of 10 mm and length of 1 m. A 100 kN force F stretches it along its length. Calculate

Concept understanding — Youngs Modulus

Young’s Modulus: The Stretchiness of a Solid

The Intuition: Stiffness per Unit Size

The Precise Definition

What the Number Tells You

A Worked Example

Q.A steel rod has a radius of 10 mm and length of 1 m. A 100 kN force F stretches it along its length. Calculate

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