Board-style MCQs and past-paper numericals in the BIEK / Sindh Board pattern. Tap an option to check yourself instantly. Solved questions are at the bottom.
Multiple-choice questions
Solved numericals (past papers)
Young's modulus of a stretched wire
A wire of length 2.0 m and cross-sectional area 1.0 × 10⁻⁶ m² stretches by 1.0 mm under a load of 100 N. Find Young's modulus.
Stress = F/A = 100 / (1.0 × 10⁻⁶) = 1.0 × 10⁸ N/m²
Strain = ΔL/L = (1.0 × 10⁻³) / 2.0 = 5.0 × 10⁻⁴
Y = stress/strain = (1.0 × 10⁸) / (5.0 × 10⁻⁴) = 2.0 × 10¹¹ N/m²
Extension from a known Young's modulus
A steel wire (Y = 2.0 × 10¹¹ N/m²) of length 4.0 m and area 2.0 × 10⁻⁶ m² carries a 200 N load. Find the extension.
ΔL = FL / (AY) = (200 × 4.0) / (2.0 × 10⁻⁶ × 2.0 × 10¹¹)
= 800 / (4.0 × 10⁵) = 2.0 × 10⁻³ m = 2.0 mm
Stress on a supporting cable
A load of 5000 N hangs from a cable of diameter 4.0 mm. Find the tensile stress.
A = πr² = π(2.0 × 10⁻³)² = 1.26 × 10⁻⁵ m²
Stress = F/A = 5000 / (1.26 × 10⁻⁵) = 3.97 × 10⁸ N/m²
Elastic potential energy stored in a wire
A wire is stretched 2.0 mm by a force of 80 N (it obeys Hooke's law). Find the strain energy stored.
E = ½ F ΔL = ½ × 80 × (2.0 × 10⁻³)
= ½ × 0.16 = 0.08 J
Force constant of a wire
A wire extends by 0.5 mm under a 40 N load (within its elastic limit). Find its force constant k.
k = F/ΔL = 40 / (0.5 × 10⁻³)
= 40 / (5.0 × 10⁻⁴) = 8.0 × 10⁴ N/m
Strain produced in a rod
A force produces a stress of 1.5 × 10⁸ N/m² in a copper rod (Y = 1.2 × 10¹¹ N/m²). Find the strain.
Strain = stress / Y = (1.5 × 10⁸) / (1.2 × 10¹¹)
= 1.25 × 10⁻³ (0.125 %)