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Is stress a vector quantity?

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प्रश्न

Is stress a vector quantity?

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उत्तर

Stress = Magnitude of internal reaction force/Area of cross-section

Hence, stress is not a scalar quantity not a vector quantity, it is a tensor quantity.

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पाठ 9: Mechanical Properties of Solids - Exercises [पृष्ठ ६९]

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एनसीईआरटी एक्झांप्लर Physics Exemplar [English] Class 11
पाठ 9 Mechanical Properties of Solids
Exercises | Q 9.15 | पृष्ठ ६९

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 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 cmis 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.


The ratio stress/strain remain constant for small deformation of a metal wire. When the deformation is made larger, will this ratio increase or decrease?


When a block a mass M is suspended by a long wire of length L, the elastic potential potential energy stored in the wire is `1/2`  × stress × strain × volume. Show that it is equal to `1/2`  Mgl, where l is the extension. The loss in gravitational potential energy of the mass earth system is Mgl. Where does the remaining `1/2` Mgl energy go ? 


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?


A wire can sustain the weight of 20 kg before breaking. If the wire is cut into two equal parts, each part can sustain a weight of 


When a metal wire is stretched by a load, the fractional change in its volume ∆V/V is proportional to


Answer in one sentence.

Define strain.


Answer in one sentence.

How should be a force applied on a body to produce shearing stress?


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.


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 ______.


A wire is suspended from the ceiling and stretched under the action of a weight F suspended from its other end. The force exerted by the ceiling on it is equal and opposite to the weight.

  1. Tensile stress at any cross section A of the wire is F/A.
  2. Tensile stress at any cross section is zero.
  3. Tensile stress at any cross section A of the wire is 2F/A.
  4. Tension at any cross section A of the wire is F.

A rod of length l and negligible mass is suspended at its two ends by two wires of steel (wire A) and aluminium (wire B) of equal lengths (Figure). The cross-sectional areas of wires A and B are 1.0 mm2 and 2.0 mm2, respectively.

(YAl = 70 × 109 Nm−2 and Ysteel = 200 × 109 Nm–2)

  1. Mass m should be suspended close to wire A to have equal stresses in both the wires.
  2. Mass m should be suspended close to B to have equal stresses in both the wires.
  3. Mass m should be suspended at the middle of the wires to have equal stresses in both the wires.
  4. Mass m should be suspended close to wire A to have equal strain in both wires.

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 ______.


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 ______.


When an elastic body is in equilibrium in its altered shape, the magnitude of the external deforming force is ______.


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