Mechanical Prop...

An Aluminium and Copper wire of same cross sectional area but having lengths in the ratio $$2 : 3$$ are joined end to end. This composite wire is hung from a rigid support and a load is suspended from the free end. If the increase in length of the composite wire is $$2.1 \ mm$$, the increase in lengths of Aluminium and Copper wires are : [$$\displaystyle { Y }_{ Al }=20\times { 10 }^{ 11 }{ N }/{ { m }^{ 2 } }$$ and $$\displaystyle { Y }_{ Cu }=12\times { 10 }^{ 11 }{ N }/{ { m }^{ 2 } }$$]

A copper wire and a steel wire of the same length and same cross section are joined end to end to form a composite wire. The composite wire is hung from a rigid support and a load is suspended from the other end. If the increase in length of the composite wire is $$2.4\ mm$$, then the increase in lengths of steel and copper wires are:

A solid sphere of radius 20cm is subjected to a uniform pressure of $$ 10^{6}$$ $$N m^{-2}$$. If the bulk modulus is $$1.7 \times 10^{11}$$ $$N m^{-2}$$, the decrease in the volume of the solid is approximately equal to:

When a metallic wire is stretched with a tension $$\displaystyle { T }_{ 1 }$$ its length is $$\displaystyle { l }_{ 1 }$$ and with a tension $$\displaystyle { T }_{ 2 }$$ its length is $$\displaystyle { l }_{ 2 }$$. The original length of the wire is:

A thick uniform rubber rope of density $$1.5\ g\ cm^{-3}$$ and Young's modulus $$5 \times 10^{6}$$ $$N m^{-2}$$ has a length of $$8 m$$. When hung from the ceiling of a room, the increase in length of the rope due to its own weight will be

When an elastic material with Young's modulus Y is subjected to stretching stress S, elastic energy stored per unit volume of the material is 

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

The rubber cord of a catapult has cross-section area $$2m{m}^{2}$$ and a total unstretched length $$15cm$$. It is stretched to $$18cm$$ and then released to project a particle of mass $$3g$$. Calculate the velocity of projection if $$Y$$ for rubber is $$8\times { 10 }^{ 8 }N/{ m }^{ 2 }$$.

The Young's modulus of a material is $$2\times { 10 }^{ 11 }N/{ m }^{ 2 }$$ and its elastic limit is $$1.8\times { 10 }^{ 8 }N/{ m }^{ 2 }$$. For a wire of $$1m$$ length of this material, the maximum elongation achievable is

A rigid bar of mass $$15 kg$$ is supported symmetrically by three wires each $$2 m$$ long. Those at each end are of copper and the middle one is of iron. Determine the ratio of their diameters if each is to have the tension? (Given E for copper = $$110\times 10^{9} N/m^{2}$$ and E for iron = $$190\times 10^{9} N/m^{2}$$).