The elastic energy stored per unit volume in a stretched wire is

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

One end of an aluminium wire whose diameter is 2.5 mm is welded to one end of a copper diameter is 1.8 mm. The composite wire carries a steady current i of I .3 A. What is the current density in each wire ?

Two wires are of same material. Wire 1 is of 4 times longer than wire 2 and area of wire 1 is 4 times less than wire 2. Compare the stresses if they are elongated by the same load

Two wires of different material but of same radius and length are stretched by the same load, the ratio of the stresses in the material will be same

Two wires of different material but of same radius and different length are stretched by the loads in the ratio 1:3, the ratio of the stresses in the material will be same

The total strain energy stored in a body is known as 

A material capable of absorbing large amount of energy before fracture is known as 

A copper wire $1.0$ m and a steel wire of length $0.5$ m having equal cross-sectional areas are joining end to end. The composite wire is stretched by a certain load which stretches the copper wire by $1$ mm. If the Young's modulus  of copper steel are respectively $1.0\times 11^{11}Nm^{-1}$ and $ 2.0 \times 10^{11} Nm^{-2}$, the total extension of the composite wire is

Give the MKS units for the following quantities.
Young's modulus.

Two wires of different materials, each $2$m long and of diameter $2\,$mm, are joined in series to form a composite wire. What force will produce a total extension of $0.9$mm. $(Y _1=2\times 10^{11}\ Pa$ & $Y _2=6\times 10^{11}\ Pa)$.

Four identical hollow cylindrical columns of steel support a big structure of mass $50,000kg$. The inner and outer radii of each column are $30\ cm$ and $60\ cm$ respectively, Assuming the load distribution to be uniform. Calculate the compressional strain of each column,

To break a wire of 1 m length, minimum 40 kg weight is required. Then the wire of the same material of double radius and 6 m length will require breaking weight 

two wires of different material, each $2m$ long and of diameter $2mm$ are joined in series to form a composite wire.What force will produce a total extension of $0.9mm$ $\left( { Y } _{ 1 }=2\times { 10 }^{ 11 }N/{ m }^{ 2 },{ Y } _{ 2 }=7\times { 10 }^{ 11 }N/{ m }^{ 2 } \right) $

Which of the following shows greater increment in length when subjected to same load to wires made of same material:

A composite wire consists of a steel Wire of length 1 5 and a co uniform cross-sectional area of ${ 2.5\times  }10^{ -5 }{ m }^{ -5 }$.It is loaded with a mass of 200kg. Find the extension produced. Young's modulus of copper is ${ 2.5\times }10^{ 11 }{ Nm }^{ -2 }$ and that of steel ${ 2.0\times  }10^{ 11 }{ Nm }^{ -2 }$

A uniform rod of length L , area of cross-section A , mass m and Young 's modulus Y is pulled on  horizontal surface by a force f , such that the friction acting on it is F/2 . What if the elongation in the rod? 

A load of 2 kg produces an extension of 1 mm in a wire of 3 m in length and 1 mm In diameter. The Young's modulus of wire will be 

A wire is suspended by one end. At the other end, a weight equivalent to 20 N force is applied. If the increase in length is I mm, then increase in the f the wire will be

Two wires of same length and same radius one of copper and another of steel are welded to form a long wire. An extension of $3cm$ is produced in it on applying a load at one of its ends. If the Young's modulus of steel is twice that of copper, then the extension in the steel wire will be

Wire of length $L$ is stretched by length l when a force $F$ is applied at one end. If elastic limit is not exceeded, the amount of energy stored in wire is 

A composite rodd consists of a steel rod of length $25cm$ and area $2A$ and a copper rod of length $50cm$ and area $A$. The composite rod is subjected to an axial load $F$. If the Young's modulii of steel and copper are in the ration $2:1$, then

Which of the following are correct?

Work done on stretching a rubber will be stored in it as :

A brass rod of length 2 m and cross-sectional area 2.0 $\displaystyle cm^{2}$ is attached end to end to a steel rod of length L and cross-sectional area 1.0 $\displaystyle cm^{2}.$ The compound rod is subjected to equal and opposite pulls of magnitude $\displaystyle 5\times 10^{4}N$ at its ends. If the elongations of the two rods are equal the length of the steel rod (L) is
($\displaystyle Y _{Brass}=1.0\times 10^{11}N/m^{2}: : and: : Y _{Steel}=2.0\times 10^{11}N/m^{2}$)

If in a wire of Young's modulus $Y$, longitudinal strain $X$ is produced then the potential energy stored in its unit volume will be :

A composite wire of a uniform cross-section $5.5\times 10^{-5}m^{2}$ consists of a steel wire of length $1.5\ m$ and a copper wire of length with a mass of $200\ kg$ is [Young's modulus of steel is $2\times 10^{11} N\ m^{-2}$ and that of copper is $1\times 10^{11}Nm^{-2}$. Take $g = 10\ ms^{-2}]$

In an experiment on the determination of Young's Modulus of a wire by Searle's method, following data is available:
Normal length of the wire (L) = $110$cm
Diameter of the wire (d) = $0.01cm$
Elongation in the wire(l) = $0.125cm$
This elongation is for a tension of $50$N. The least counts for corresponding quantities are $0.01cm, 0.00005 cm, $ and $0.001cm$, respectively. Calculate the maximum error in calculating the value of Young's modulus(Y).

When a weight of 5 kg is suspended from a copper wire of length 30 m and diameter 0.5 mm, the length of the wire increases by 2.4 cm. If the diameter is doubled, the extension produced is :

The maximum load a wire can with stand without breaking, when it is stretched to twice of its original length, will:

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

The length of an elastic string is $x$ metre when the tension is $8\ N$. Its length is $y$ metre when the tension is $10\ N$. What will be its length, when the tension is $18\ N$?

Work done by restoring force in a string within elastic limit is $-10\ J$. The maximum amount of heat produced in the string is :

If work done in stretching a wire by 1 mm is 2J. Then the work necessary for stretching another wire of same material but with double the radius and half the length by 1 mm in joule is

When a body mass $M$ is attached to power end of a wire (of length $L$) whose upper end is fixed, then the elongation of the wire is $l$. In this situation mark out the correct statement(s).