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`
APPEARS IN
संबंधित प्रश्न
A rod of length 1.05 m having negligible mass is supported at its ends by two wires of steel (wire A) and aluminium (wire B) of equal lengths as shown in Figure. The cross-sectional areas of wires A and B are 1.0 mm2 and 2.0 mm2, respectively. At what point along the rod should a mass m be suspended in order to produce (a) equal stresses and (b) equal strains in both steel and aluminium wires.
A mild steel wire of length 1.0 m and cross-sectional area 0.50 × 10–2 cm2 is stretched, well within its elastic limit, horizontally between two pillars. A mass of 100 g is suspended from the mid-point of the wire. Calculate the depression at the midpoint.
Two strips of metal are riveted together at their ends by four rivets, each of diameter 6.0 mm. What is the maximum tension that can be exerted by the riveted strip if the shearing stress on the rivet is not to exceed 6.9 × 107 Pa? Assume that each rivet is to carry one-quarter of the load.
A steel blade placed gently on the surface of water floats on it. If the same blade is kept well inside the water, it sinks. Explain.
A rope 1 cm in diameter breaks if the tension in it exceeds 500 N. The maximum tension that may be given to a similar rope of diameter 2 cm is
The breaking stress of a wire depends on
A charged particle is moving in a uniform magnetic field in a circular path of radius R. When the energy of the particle becomes three times the original, the new radius will be ______.
A spiral spring is stretched by a weight. The strain will be:
The maximum load a wire can withstand without breaking, when its length is reduced to half of its original length, will ______.
Consider a long steel bar under a tensile stress due to forces F acting at the edges along the length of the bar (Figure). Consider a plane making an angle θ with the length. What are the tensile and shearing stresses on this plane
- For what angle is the tensile stress a maximum?
- For what angle is the shearing stress a maximum?
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?
A body of mass m = 10 kg is attached to one end of a wire of length 0.3 m. The maximum angular speed (in rad s-1) with which it can be rotated about its other end in the space station is (Breaking stress of wire = 4.8 × 107 Nm-2 and the area of cross-section of the wire = 10-2 cm2) 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?
Strain is defined as the ratio of ______.
The SI unit of stress is ______.
