Stress:
When a force is applied on a body there will be relative displacement of the particles and due to property of elasticity an internal restoring force is developed which tends to restore the body to its original state.
The internal restoring force acting per unit area of cross section of the deformed body is called stress.
At equilibrium, restoring force is equal in magnitude to external force, stress can therefore also be defined as external force per unit area on a body that tends to cause it to deform.
If external force F is applied on the area A of a body then, Stress = F/A
Unit: N /m2 (S.I.) , dyne / cm2 (C.G.S.)
Dimension: [ML-1T-2]
Stress developed in a body depends upon how the external forces are applied over it.
Types of stress:
(i) Longitudinal stress (ii) Bulk or Volume stress (iii) Shear or tangential stress
Difference between Pressure and Stress
(i) Pressure is always normal to the area. Stress can be normal or tangential.
(ii) Always compressive in nature. May be compressive or tensile in nature.
Q.1. A and B are two wires. The radius of A is twice that of B. they are stretched by the same load. Then the stress on B is
(a) Equal to that on A
(b) Four times that on A
(c) Two times that on A
(d) Half that on A
Answer
(b)Q.2. One end of a uniform wire of length L and of weight W is attached rigidly to a point in the roof and a weight W1 is suspended from its lower end. If S is the area of cross-section of the wire, the stress in the wire at a height 3L/4 from its lower end is
Answer
(c)Q.3. On suspending a weight Mg, the length l of elastic wire and area of cross-section A its length becomes double the initial length. The instantaneous stress action on the wire is
(a) Mg/A
(b) Mg/2A
(c) 2Mg/A
(d) 4Mg/A
Answer
(c)Q.4. A bar is subjected to equal and opposite forces as shown in the figure. PQRS is a plane making angle θ with the cross-section of the bar. If the area of cross-section be ‘A’, then what is the tensile stress on PQRS
(a) F / A
(b) F cosθ / A
(c) F cos2θ / A
(d) F / A cosθ
Answer
(c)Q.5. In the above question, what is the shearing stress on PQ
(a) F / A cos θ
(b) F sin 2θ / 2A
(c) F / 2A sin 2θ
(d) F cosθ / A
Answer
(b)Q.6. In the above question, when is the tensile stress maximum
(a) θ=00
(b) θ=300
(c) θ=450
(d) θ=900
Answer
(a)Q.7. In the above question, when is the shearing stress maximum
(a) θ=00
(b) θ=300
(c) θ=450
(d) θ=900
Answer
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