Advertisements
Advertisements
प्रश्न
A rigid bar of mass 15 kg is supported symmetrically by three wires each 2.0 m long. Those at each end are of copper and the middle one is of iron. Determine the ratio of their diameters if each is to have the same tension.
Advertisements
उत्तर १
The tension force acting on each wire is the same. Thus, the extension in each case is the same. Since the wires are of the same length, the strain will also be the same.
The relation for Young’s modulus is given as:
`Y = "Stress"/"Strain" = (F/A)/"Strain" = ((4F)/(pid^2))/"Strain"` .....(i)
Where,
F = Tension force
A = Area of cross-section
d = Diameter of the wire
It can be inferred from equation (i) that `Y prop 1/d^2`
Young’s modulus for iron, Y1 = 190 × 109 Pa
Diameter of the iron wire = d1
Young’s modulus for copper, Y2 = 120 × 109 Pa
Diameter of the copper wire = d2
Therefore, the ratio of their diameters is given as:
`d_2/d_1 = sqrt(Y_1/Y_2) = sqrt((190xx10^9)/(120xx10^9)) = sqrt(19/12) = 1:25:1`
उत्तर २
Since each wire is to have same tension, therefore, each wire has the same extension. Moreover, each wire has the same initial length.So, the strain is same for each wire.
Now, `Y = "Stress"/"Strain" = (F/((piD^2)/4))/"Strain"`
or `Y prop 1/D^2 => D prop 1/sqrtY`
`D_"copper"/(D_"iron") = sqrt((Y_""iron)/(Y_"copper")) = sqrt((190 xx 10^9)/(110 xx 10^9)) = sqrt(19/11) =1.314`
संबंधित प्रश्न
Determine the volume contraction of a solid copper cube, 10 cm on an edge, when subjected to a hydraulic pressure of 7.0 ×106 Pa.
The yield point of a typical solid is about 1%. Suppose you are lying horizontally and two persons are pulling your hands and two persons are pulling your legs along your own length. How much will be the increase in your length if the strain is 1% ? Do you think your yield point is 1% or much less than that?
Answer in one sentence.
Define strain.
A rod has a radius of 100 mm and a length of 10 cm. A 100 N force compress along its length. Calculate the longitudinal stress developed in the rod.
Modulus of rigidity of ideal liquids is ______.
Modulus of rigidity of ideal liquids is ______.
The maximum load a wire can withstand without breaking, when its length is reduced to half of its original length, will ______.
A spring is stretched by applying a load to its free end. The strain produced in the spring is ______.
A mild steel wire of length 2L and cross-sectional area A is stretched, well within elastic limit, horizontally between two pillars (Figure). A mass m is suspended from the mid point of the wire. Strain in the wire is ______.
Is stress a vector quantity?
The value of tension in a long thin metal wire has been changed from T1 to T2. The lengths of the metal wire at two different values of tension T1 and T2 are l1 and l2 respectively. The actual length of the metal wire is ______.
A steel wire having a radius of 2.0 mm, carrying a load of 4 kg, is hanging from a ceiling. Given that g = 3.1πms-2, what will be the tensile stress that would be developed in the wire?
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 ______.
Answer in one sentence:
What is an elastomer?
What is the physical quantity defined as the internal restoring force per unit area of a body?
The SI unit of stress is:
What are the dimensions of strain?
