Mechanical Prop...

A uniform pressure P is exerted on all sides of a solid cube at temperature t $$^oC$$. By what amount should the temperature of the cube be raised in order to bring its volume back to the value it had before the pressure was applied? The coefficient of volume expansion of cube is $$\alpha$$ and the bulk modulus is K.

Two wires are made of the same material and have the same volume. However $$wire\ 1$$ has cross-sectional area $$A$$ and $$wire\ 2$$ has cross-sectional area $$3A.$$ If the length of $$wire\ 1$$ is increases by $$\Delta x$$ on applying force $$F,$$ how much force is needed to stretch $$wire\ 2$$ by the same amount?

The ice storm in the state of Jammu strained many wires to the breaking point. In a particular situation, the transmission towers are separated by $$500\ m$$ of wire. The top grounding wire $$15^{o}$$ from horizontal at the towers, and has a diameter of $$1.5cm$$. The steel wire has a density of $$7860\ kg\ m^{-3}$$. When ice (density $$900\ kg\ m^{-3}$$) built upon the wire to a diameter $$10.0\ cm$$, the wire snapped. What was the breaking stress (force/ unit area) in $$N\ m^{-2}$$ in the wire at the breaking point? You may assume the ice has no strength.

A wire suspended vertically from one of its ends stretched by attaching weight of $$200$$ N to the lower end. The weight stretches the wire by$$ 1 $$mm. Then the elastic energy stored in the wire is  

Two wires of the same radius and material and having length in the ratio $$8.9:7.6$$ are stretched by the same force. The strains produced in the two cases will be in the ratio:

Breaking stress for steel is $$F/A$$, where $$A$$ is the area of cross-section of steel wire. A body of mass $$M$$ is tied at the end of the steel wire of length $$L$$ and whirled in a horizontal circle. The maximum number of revolution it can make per second is:

A spherical ball contracts in volume by $$0.01\%$$ when subjected to a normal uniform pressure of $$100$$ atmospheres. The bulk modulus of its material in dynes$$/cm^2$$ is?

The length of a wire increases by $$8mm$$ when a weight of $$5kg$$ is suspended from it. If other things remain the same but the radius of the wire is doubled, what will be the increase in its length?

A uniform rod of mass m and length $$l$$ is rotating with constant angular velocity $$\omega$$ about an axis which passes through its one end and perpendicular to the length of rod. The area of cross section of the rod is A and its young's modulus is Y. Neglect gravity. The strain at the mid point of the rod is :

A uniform wire of length $$L$$ and radius $$r$$ is twisted by an angle $$\alpha$$. If modulus of rigidity of the wire is $$\eta$$, then the elastic potential energy stored in wire, is