Mechanical Prop...

A brass rod has a length of $$0.2m$$, area of cross section 1.0cm$$^{2}$$ and young's modulus 10$$^{11}$$ Nm$$^{-2}$$. If it is compressed by $$5kg$$ weight along its length, then the change in its energy will be :

A solid sphere of radius $$R$$ made of 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 liquid. When a mass $$m$$ is placed on the piston to compress the liquid, the fractional change in the radius of the sphere $$\delta R/R$$ is :

A spring of spring constant 5 x 10$$^{3}$$Nm$$^{-1}$$ is stretched initially by $$5 cm$$ from the unstretched position. Then the work required to stretch it further by another $$5 cm$$ is       

A $$20 kg$$ load is suspended from the lower end of a wire $$10 cm$$ long and $$1 mm$$$$^2$$ in cross sectional area. The upper half of the wire is made of iron and the lower half with aluminium. The total elongation in the wire is
($$Y_{iron} =$$ 20 x 10$$^{10}$$ N/m$$^{2}$$, $$Y_{Al}$$ $$=$$ 7 x 10$$^{10}$$ N/m$$^{2}$$)

The length of a metal wire is $$l_{1}$$ when the tension in it is $$F_{1}$$ and $$l_{2}$$ when the tension in it is $$F_{2}$$. The natural length of the wire is

A uniform metal rod of $$2mm$$$$^{2}$$ cross section is heated from 0$$^{o}$$C to 20$$^{o}$$C. The coefficient of linear expansion of the rod is 12 x 10$$^{-6/0}$$C. Its Young's modulus of elasticity is 10$$^{11}$$ N/m$$^{2}$$. The energy stored per unit volume of the rod is :

A piece of copper wire has twice the radius of steel wire. One end of the copper wire is joined to one end of steel wire so that both of them can be subjected to the same longitudinal force. $$Y$$ for steel is twice that of copper. When the length of copper wire is increased by $$1$$%, the steel wire will be stretched by

One end of uniform wire of length $$L$$ and of weight $$W$$ is attached rigidly to a point in the roof and a weight $$W_{1}$$ is suspended from the lower end. If $$A$$ is the area of cross-section of the wire, the stress in the wire at a height $$\dfrac{3L}{4}$$ from its lower end is:

The length of an elastic spring is '$$a$$' when tension is $$4 N$$ and '$$b$$' when the tension is $$5N$$. The length of the spring when tensionis 9N is

A steel wire of length 5m is pulled to have an extension of 1mm. Its Y is 1.9 x 10$$^{4}$$ N/m$$^{2}$$. The energy per unit volume stored in it is