Mechanical Prop...

$$32 g$$ of $$O_{2}$$ is contained in a  cubical container  of side $$1 m$$  and  maintained at a temperature of $$127 ^{0} C$$. The isothermal bulk modulus of elasticity of the gas in terms of universal gas constant $$R$$ is

A uniform cylindrical wire is subjected to a longitudinal tensile stress of $$5\times 10^{7} N/m^{2}$$. Young's modulus of the material of the wire is $$2\times 10^{11} N/m^{2}$$. The volume change in the wire is $$0.02\%$$. The fractional change in the radius is

Find how the volume density of the elastic deformation energy is distributed in a steel rod depending on the distance $$r$$ from its axis. The length of the rod is equal to $$l$$, the torsion angle to $$\varphi$$.

A copper rod of length $$l$$ is suspended from the ceiling by one of its ends. Find the elongation $$\Delta l$$ of the rod due to its own weight.

The length of a metal is $$l_1$$ when the tension in it is $$T_1$$ and is $$l_2$$ when the tension is $$T_2$$. The original length of the wire is  :

In Searle's experiment to find Young's modulus the diameter of wire is measured as $$d=0.05cm$$, length of wire is $$l=125cm$$ and when a weight,$$m=20.0kg$$ is put, extension in wire was found to be $$0.100cm$$. Find the maximum permissible error in Young's modulus $$(Y)$$. Use:$$Y=\displaystyle\frac{mgl}{(\pi/4)d^2x}$$.

 Young's modulis of brass and steel are  $$10 \times 10^{10}\ N/m$$ and $$2\times 10^{11}\ N/m^2$$, respectively. A brass wire and a steel wire of the same length are extended by $$1mm$$ under the same force. The radii of brass and steel wires are $$R_B$$ and $$R_S$$ respectively. Then

If the ratio of lengths, radii and Young's modulus of steel and brass wires shown in the figure are a, b and c respectively, the ratio between the increase in lengths of brass and steel wires would be :

A tension of $$20\  N$$ is applied to a copper wire of cross sectional area $$0.01 cm^2$$, Young's Modulus of copper is $$1.1\times 10^{11} N/m^2$$ and Poisson's ratio is 0.32. The decrease in cross sectional area of the wire is:

The length of a metal wire is $$l_1$$ when the tension in it is $$F_1$$ and $$l_2$$ when the tension is $$F_2$$. Then original length of the wire is: