Advertisements
Advertisements
Question
The temperature of a wire is doubled. The Young’s modulus of elasticity ______.
Options
will also double.
will become four times.
will remain same.
will decrease.
Advertisements
Solution
The temperature of a wire is doubled. The Young’s modulus of elasticity will decrease.
Explanation:
Young's modulus (Y): It is defined as the ratio of normal stress to longitudinal strain within the limit of proportionality.
`Y = "Normal stress"/"Longitudinal strain"`
= `(F/A)/((ΔL)/L)`
= `(FL)/(AΔL)`
The fractional change in length of any material is defined as `(ΔL)/L_0 = αΔT` where ΔT is the change in the temperature, L0 is the original length, α is the coefficient of linear expansion of the given material and L0 is the original length of material.
So, simply a change in length is due to change in temperature.
`ΔL = L_0αΔT`
And Young's modules
(Y) = `"Stress"/"Strain"`
= `(FL_0)/(A xx ΔL)`
= `(FL_0)/(AL_0 ΔT) ∝ 1/(ΔT)`
As Y ∝ 1/∆T
When temperature increases ∆T increases, hence Y decreases.
APPEARS IN
RELATED QUESTIONS
Four identical hollow cylindrical columns of mild steel support a big structure of mass 50,000 kg. 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.
A 14.5 kg mass, fastened to the end of a steel wire of unstretched length 1.0 m, is whirled in a vertical circle with an angular velocity of 2 rev/s at the bottom of the circle. The cross-sectional area of the wire is 0.065 cm2. Calculate the elongation of the wire when the mass is at the lowest point of its path.
Two wires A and B are made of same material. The wire A has a length l and diameter rwhile the wire B has a length 2l and diameter r/2. If the two wires are stretched by the same force, the elongation in A divided by the elongation in B is
The length of a metal wire is l1 when the tension in it T1 and is l2 when the tension is T2. The natural length of the wire is
A student plots a graph from his reading on the determination of Young modulus of a metal wire but forgets to put the labels. the quantities on X and Y-axes may be respectively
(a) weight hung and length increased
(b) stress applied and length increased
(c) stress applied and strain developed
(d) length increased and the weight hung.
A copper wire of cross-sectional area 0.01 cm2 is under a tension of 20N. Find the decrease in the cross-sectional area. Young modulus of copper = 1.1 × 1011 N m−2 and Poisson ratio = 0.32.
`["Hint" : (Delta"A")/"A"=2(Delta"r")/"r"]`
A uniform rectangular block of mass of 50 kg is hung horizontally with the help of three wires A, B and C each of length and area of 2m and 10mm2 respectively as shown in the figure. The central wire is passing through the centre of gravity and is made of material of Young's modulus 7.5 x 1010 Nm−2 and the other two wires A and C symmetrically placed on either side of the wire B are of Young's modulus 1011 Nm−2 The tension in the wires A and B will be in the ratio of:
Young's modulus of a perfectly rigid body is ______.
The temperature of a wire is doubled. The Young’s modulus of elasticity ______.
The Young’s modulus for steel is much more than that for rubber. For the same longitudinal strain, which one will have greater tensile stress?
Identical springs of steel and copper are equally stretched. On which, more work will have to be done?
A truck is pulling a car out of a ditch by means of a steel cable that is 9.1 m long and has a radius of 5 mm. When the car just begins to move, the tension in the cable is 800 N. How much has the cable stretched? (Young’s modulus for steel is 2 × 1011 Nm–2.)
If the yield strength of steel is 2.5 × 108 Nm–2, what is the maximum weight that can be hung at the lower end of the wire?
In nature, the failure of structural members usually result from large torque because of twisting or bending rather than due to tensile or compressive strains. This process of structural breakdown is called buckling and in cases of tall cylindrical structures like trees, the torque is caused by its own weight bending the structure. Thus the vertical through the centre of gravity does not fall within the base. The elastic torque caused because of this bending about the central axis of the tree is given by `(Ypir^4)/(4R) . Y` is the Young’s modulus, r is the radius of the trunk and R is the radius of curvature of the bent surface along the height of the tree containing the centre of gravity (the neutral surface). Estimate the critical height of a tree for a given radius of the trunk.
If the length of a wire is made double and the radius is halved of its respective values. Then, Young's modules of the material of the wire will ______.
What is longitudinal strain?
Which of the following statements about Young's modulus is correct?
