Advertisements
Advertisements
प्रश्न
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?
Advertisements
उत्तर
`L_t - L_0 (1 + aΔt)`
`L_t - L_0 = L_0a xx Δt)`
`ΔL = 1 xx 10^-5 xx 200 = 2 xx 10^-3`
`Y = (FL_0)/(AΔL)`
`L_0 = 1 m`
`F = (YAΔL)/L_0`
`A = 1 cm^2 = 10^-4m^2`
`Y = 2 xx 10^11 Nm^2`
`ΔL = 2 xx 10^-3 m`
`F = (2 xx 10^11 xx 10^-4 xx 2 xx 10^3)/1`
= `4 xx 10^-7`
= `4 xx 10^4` N
APPEARS IN
संबंधित प्रश्न
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?
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 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.
The temperature of a wire is doubled. The Young’s modulus of elasticity ______.
The temperature of a wire is doubled. The Young’s modulus of elasticity ______.
A rigid bar of mass M is supported symmetrically by three wires each of length l. Those at each end are of copper and the middle one is of iron. The ratio of their diameters, if each is to have the same tension, is equal to ______.
Identical springs of steel and copper are equally stretched. On which, more work will have to be done?
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.
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?
Which of the following statements about Young's modulus is correct?
In the formula Y = MgL/(πr²l), what does 'l' represent?
The maximum elongation of a steel wire of 1 m length if the elastic limit of steel and its Young’s modulus, respectively, are 8 × 108 Nm−2 and 2 × 1011 Nm−2, is ______.
