Mechanical Properties of Solids

A wire of length 1 m and area 3×10⁻⁶ m² stretches by 0.5 mm under a 900 N load. Find Young's modulus.

A uniform wire of mass 3 kg, length 6 m, area 2×10⁻⁶ m², and Young's modulus 1×10¹¹ Pa hangs vertically. Find its elongation due to its own weight. (g = 10 m/s²)

A material is stressed to 4×10⁸ Pa with Young's modulus 4×10¹¹ Pa. Find the elastic energy stored per unit volume.

A block's volume decreases by 0.05% under a pressure increase of 5×10⁶ Pa. Find the bulk modulus.

Two identical wires of Young's moduli 3×10¹¹ Pa and 1×10¹¹ Pa are stretched by the same force. Find the ratio of their elongations (first : second).

A wire has longitudinal strain 0.004 and Poisson's ratio 0.25. Find its lateral strain.

Find the force needed to stretch a wire (Y = 2×10¹¹ Pa, A = 1×10⁻⁶ m², L = 2 m) by 2 mm.

A material with Young's modulus 1.5×10¹¹ Pa is subjected to a strain of 0.001. Find the stress.

A wire of volume 2×10⁻⁴ m³ is stressed to 1×10⁸ Pa with Young's modulus 1×10¹¹ Pa. Find the total elastic potential energy stored.

A material has bulk modulus 2×10⁹ Pa. Find the percentage decrease in volume under a pressure increase of 4×10⁶ Pa.

A material has shear stress 2×10⁶ Pa and shear strain 0.0004. Find its modulus of rigidity.

Wire A (length 2 m, area 1×10⁻⁶ m²) and wire B (length 4 m, area 2×10⁻⁶ m²) are made of the same material and stretched by the same force. Find the ratio of their elongations (A : B).