Advertisements
Advertisements
प्रश्न
The temperature of a wire is doubled. The Young’s modulus of elasticity ______.
पर्याय
will also double.
will become four times.
will remain same.
will decrease.
Advertisements
उत्तर
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
संबंधित प्रश्न
A steel wire of length 4.7 m and cross-sectional area 3.0 × 10–5 m2 stretches by the same amount as a copper wire of length 3.5 m and cross-sectional area of 4.0 × 10–5 m2 under a given load. What is the ratio of Young’s modulus of steel to that of copper?
The figure shows the strain-stress curve for a given material. What are (a) Young’s modulus and (b) approximate yield strength for this material?
Read the following statements below carefully and state, with reasons, if it is true or false
The Young’s modulus of rubber is greater than that of steel;
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.
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
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 steel rod of cross-sectional area 4 cm2 and 2 m shrinks by 0.1 cm as the temperature decreases in night. If the rod is clamped at both ends during the day hours, find the tension developed in it during night hours. Young modulus of steel = 1.9 × 1011 N m−2.
Identical springs of steel and copper are equally stretched. On which, more work will have to be done?
A steel rod (Y = 2.0 × 1011 Nm–2; and α = 10–50 C–1) of length 1 m and area of cross-section 1 cm2 is heated from 0°C to 200°C, without being allowed to extend or bend. What is the tension produced in the rod?
A steel rod of length 2l, cross sectional area A and mass M is set rotating in a horizontal plane about an axis passing through the centre. If Y is the Young’s modulus for steel, find the extension in the length of the rod. (Assume the rod is uniform.)
A metal wire of length L, area of cross section A and Young's modulus Y behaves as a spring of spring constant k given by:
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 ______.
The force required to stretch a wire of cross section 1 cm2 to double its length will be ______.
(Given Young's modulus of the wire = 2 × 1011 N/m2)
Young's modulus is also known as
What does the dimensional formula [L⁻¹M¹T⁻²] represent?
What is longitudinal strain?
