A bridge can bear 4 x 10⁴ kg weight. If the breaking stress is 47 x 10³ N/m³ and factor of safety is 5 then the area of cross section of the rod will be : 

The Poisson's ratio for a material is 0.1. If the longitudinal strain of a rod of this material is 1 x 10^-3, then the percentage change in the volume of rod will be :

A thick rope of density 'ρ' and length 'L' is hung from a rigid support. The Young's modulus of the material of rope is 'Y'. The increase in length of the rope due to its own weight is :

A 5 m long steel wire is suspended from the ceiling of a room. A sphere of mass 25 kg and 10 cm radius is attached to another end of the wire. The  height of the ceiling is 5.21 m. When the sphere is made to oscillate as a pendulum, then its lowest point just touches the floor. The velocity of the sphere at the lowest point will be : 

(Given : Y = 2 x 10¹¹N/m², radius of wire = 0.05 cm)

For the same cross-sectional area and for a given load, the ratio of depressions for the beam of a square cross-section and circular cross-section is :

Two rods of different materials having coefficients of linear expansion α₁ and α₂ , Young's modulii Y₁ and Y₂ respectively are fixed between two rigid massive walls. The rods are heated such that they undergo the same increase in temperature. There is no bending of rods. If α₁ : α₂ =2 : 3, the thermal stresses developed in the two rods are equal provided Y₁ : Y₂ is equal to :

The magnitude of the force developed by raising the temperature from 0^oC to 100^oC of the iron bar 1.00 m long and 1 cm² cross-section when it is held so that it is not permitted to expand or bend is :

(Given : α = 10^-5 /^oC and Y = 10¹¹ N/m²)

The volume of a solid rubber ball when it is carried from the surface to the bottom of a 200 m deep lake decreases by 0.1%. The value for bulk modulus of elasticity for rubber will be :

The bulk modulus of rubber is 9 x 10⁸ N/m². To what depth below the surface of sea should the rubber ball taken as to decrease its volume by 0.1%?