Advertisements
Advertisements
प्रश्न
The temperature of a wire is doubled. The Young’s modulus of elasticity ______.
विकल्प
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?
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.
A wire elongates by 1.0 mm when a load W is hung from it. If this wire goes over a a pulley and two weights W each are hung at the two ends, he elongation of he wire will be
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 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.
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:
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 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 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.)
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 ______.
Young's modulus is also known as ______.
What does the dimensional formula [L⁻¹M¹T⁻²] represent?
What is longitudinal strain?
In the formula Y = MgL/(πr²l), what does 'l' represent?
