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Is stress a vector quantity? - Physics

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

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.


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.


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 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


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 


A load of 10 kg is suspended by a metal wire 3 m long and having a cross-sectional area 4 mm2. Find (a) the stress (b) the strain and (c) the elongation. Young modulus of the metal is 2.0 × 1011 N m−2

 

Answer in one sentence.

Define strain.


Answer in one sentence.

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


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.

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(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.

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 ______.


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 an elastomer?


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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