Mechanical Prop...

Two wires having same length and material are stretched by same force. Their diameters are in the ratio 1 : 3. The ratio of strain energy per unit volume for these two wires (smaller to larger diameter) when stretched is

A steel wire of length $$4.5m$$ and cross-sectional area $$3\times { 10 }^{ -5 }{ m }^{ 2 }$$ stretches by the same amount as a copper wire of length $$3.5m$$ and cross-sectional area of $$4\times { 10 }^{ -5 }{ m }^{ 2 }$$ under a given load. The ratio of the Young's modulus of steel to that of copper is:

A given quantity of an ideal gas is at pressure P and absolute temperature T. The isothermal bulk modulus of the gas is?

A brass rod of length $$1 \ m$$ is fixed to a vertical wall at one end, with the other end keeping free to expand. When the temperature of the rod is increased by $$120^{\circ}C$$ , the length increases by $$3 \ cm$$. What is the strain? 

An amusement park ride consists of airplane shaped cars attached to steel rods. Each rod has a length of 20.0 m and a cross-sectional area of 8.00 $$cm^2$$. Young's modulus for steel is $$2 \, \times \, 10^{11} \, N/m^2.$$
b. When operating, the ride has a maximum angular speed of $$\sqrt{1}$$9/5 rad/s. How much is the rod stretched (in mm) then? 

Two metal wire 'P' and 'Q' of same length and material are stretched by same load. Their masses are in the ratio $$m_1 : m_2$$. The ratio of elongations of wire 'P' to that of 'Q' is

A solid sphere of radius $$R$$, made up of a material of bulk modulus $$K$$ is surrounded by a liquid in a cylindrical container. A massless piston of area $$A$$ floats on the surface of the liquid. When a mass $$M$$ is placed on the piston to compress the liquid, the fractional change in the radius of the sphere is

If the ratio of diameters, lengths and Young's moduli of steel and brass wires shown in the figure are $$p,q$$ and $$r$$ respectively. Then the corresponding ratio of increase in their lengths would be:

A student performs an experiment to determine the Young's modulus of a wire, exactly $$2m$$ long, by Searle's method. In a particular reading, the student measures the extension in the length of the wire to be $$0.8$$mm with an uncertainty of $$0.05 mm$$ at a load of exactly $$1.0$$kg. The student also measures the diameter of the wire to be $$0.4mm$$ with an uncertainty of $$0.01mm$$. Take $$g = 9.8 m s^{-2}$$ (exact). The Young's modulus obtained from the reading is:

A load is supported using three wires of same cross section area as shown. Then for :