Properties of Matter

Young's moduli of two wires A and B are in the ratio 7 : 4. Wire A is 2 m long and has radius R. Wire B is 1.5 m long and has radius 2 mm. If the two wires stretch by the same length for a given load, then the value of R is close to :-

In an experiment, brass and steel wires of length 1 m each with areas of cross section 1mm² are used. The wires are connected in series and one end of the combined wire is connected to a rigid support and other end is subjected to elongation. The stress required to produce a net elongation of 0.2 mm is, [Given, the Young's Modulus for steel and brass are, respectively, 120 × 10⁹ N/m² and 60 × 10⁹ N/m²]

A uniform cylindrical rod of length L and radius r, is made from a material whose Young’s modulus of Elasticity equals Y. When this rod is heated by temperature T and simultaneously subjected to a net longitudinal compressional force F, its length remains unchanged. The coefficient of volume expansion, of the material of the rod, is (nearly) equal to :

A cube of metal is subjected to a hydrostatic pressure of 4 GPa. The percentage change in the length of the side of the cube is close to : (Given bulk modulus of metal, B = 8 $$\times$$ 10¹⁰ Pa)

An object of mass m is suspended at the end of a massless wire of length L and area of crosssection A. Young modulus of the material of the wire is Y. If the mass is pulled down slightly its frequency of oscillation along the vertical direction is :

If Y, K and $$\eta$$ are the values of Young's modulus, bulk modulus and modulus of rigidity of any material respectively. Choose the correct relation for these parameters.

The normal density of a material is $$\rho$$ and its bulk modulus of elasticity is K. The magnitude of increase in density of material, when a pressure P is applied uniformly on all sides, will be :

The length of metallic wire is l₁ when tension in it is T₁. It is l₂ when the tension is T₂. The original length of the wire will be :

The value of tension in a long thin metal wire has been changed from T₁ to T₂. The lengths of the metal wire at two different values of tension T₁ and T₂ are l₁ and l₂ respectively. The actual length of the metal wire is :

The length of a metal wire is l₁, when the tension in it is T₁ and is l₂ when the tension is T₂. The natural length of the wire is :