Mechanical Prop...

If $$S$$ is stress and $$Y$$ is Young's modulus of material of wire, then energy stored in the wire per unit volume is:

A long spring is stretched by $$2   cm$$ and its potential energy is $$U$$. If the spring is stretched by $$10   cm$$; its potential energy will be (in terms of $$U$$)

Longitudinal strain is possible in 

The adjacent graph shows the extension ($$\displaystyle \Delta l$$) of a wire of length 1 m suspended from the top of a . roof at one end and with a load W connected to the other end. If the cross-sectional area of the wire is $$\displaystyle { 10 }^{ -6 }{ m }^{ 2 }$$, calculate the Young's modulus of the material of the wire.

For a given material, the Young's modulus is $$2.4$$ times that of rigidity modulus. Its poisson's ratio is.

For a constant hydraulic stress on an object, the fractional change in the object's volume ($$\displaystyle \Delta { V }/{ V }$$) and its bulk modulus (B) are related as: 

The length of an elastic string is $$a$$ metre when the longitudinal tension is $$4$$N and $$b$$ metre when the longitudinal tension is $$5$$N. The length of the string in metre when longitudinal tension is $$ 9 $$N is :

A $$5$$m long aluminium wire $$(Y=7\times 10^{10}Nm^{-2})$$ of diameter $$3$$mm supports a $$40$$kg mass. In order to have the same elongation in the copper wire $$(Y=12\times 10^{10}Nm^{-2})$$ of the same length under the same weight, the diameter should now be (in mm).

If a wire having initial diameter of $$2   mm$$ produced the longitudinal strain of $$0.1$$%, then the final diameter of wire is $$\left( \sigma = 0.5 \right)$$

The length of a metal wire is $$L_1$$ when the tension is $$T_1$$ and $$L_2$$ when the tension is $$T_2$$. The unstretched length of wire is :