The figure given below shows the longitudinal stress vs longitudinal strain graph for a given material. Based on the given graph, Young's modulus of the material with the increase in strain will:

        

1. be variable.

2. first increase & then decrease.

3. first decrease & then increase.

4. remain constant.

Subtopic:  Stress - Strain Curve |
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The figure shows the stress-strain curve for a given material. Young's modulus for the material is:
     

1 7.5×1010 N m-2
2 5×1010 N m-2
3 7.5×109 N m-2
4 7.5×108 N m-2

Subtopic:  Stress - Strain Curve |
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A student plots a graph from his readings on the determination of Young modulus of a metal wire but forgets to put the labels (figure). The quantities on X and Y-axes may be respectively,

               

(a) weight hung and length increased
(b) stress applied and length increased
(c) stress applied and strain developed
(d) length increased and the weight hung


Choose the correct option:

1. (a) and (b)
2. (b) and (c)
3. (a), (b) and (d)
4. all of these
Subtopic:  Young's modulus |
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A copper and a steel wire of the same diameter are connected end to end. A deforming force \(F\) is applied to this composite wire which causes a total elongation of \(1\) cm. The two wires will have:

a. the same stress
b. different stress
c. the same strain
d. different strain

Choose the correct option:

1. (a, b)
2. (a, d)
3. (b, c)
4. (c, d)

Subtopic:  Young's modulus |
 78%
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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 N/m2 and Ysteel=200×109 N/m2)



 

(a) Mass m should be suspended close to wire A to have equal stresses in both wires.
(b) Mass m should be suspended close to B to have equal stresses in both wires.
(c) Mass m should be suspended in the middle of the wires to have equal stresses in both wires.
(d) Mass m should be suspended close to wire A to have equal strain in both wires.

The correct statements are:

1. (b, c)

2. (a, d)

3. (b, d)

4. (c, d)

Subtopic:  Elasticity | Stress - Strain |
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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.

(a) Tensile stress at any cross-section \(A\) of the wire is \(F/A.\)
(b) Tensile stress at any cross-section is zero.
(c) Tensile stress at any cross-section \(A\) of the wire is \(2F/A.\)
(d) Tension at any cross-section \(A\) of the wire is \(F.\)

The correct statements are:
1. (a), (b)
2. (a), (d)
3. (b), (c)
4. (a), (c)

Subtopic:  Stress - Strain |
 80%
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The stress-strain graphs for the two materials are shown in the figure. (assumed same scale)

    

(a) Material (ii) is more elastic than material (i) and hence material (ii) is more brittle
(b) Material (i) and (ii) have the same elasticity and the same brittleness
(c) Material (ii) is elastic over a larger region of strain as compared to (i)
(d) Material (ii) is more brittle than material (i)


The correct statements are:

1. (a, c)
2. (c, d)
3. (b, c)
4. (b, d)

Subtopic:  Stress - Strain Curve |
 71%
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A large cylindrical piece of a dense solid elastic metal stands on its end as shown in the figure. The metal is uniform and isotropic. The stress in the material as a function of height is shown correctly by:
   
1.   2.
3.  4. 
Subtopic:  Stress - Strain Curve |
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Given below are two statements: 
Assertion (A): Soft steel can be made red hot by continued hammering on it, but hard steel cannot.
Reason (R): Energy transfer in the case of soft is large as in hard steel.
 
1. Both (A) and (R) are true and (R) is the correct explanation of (A).
2. Both (A) and (R) are true but (R) is not the correct explanation of (A).
3. (A) is true but (R) is false.
4. (A) is false but (R) is true.


 
Subtopic:  Potential energy of wire |
 80%
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Given below are two statements: 
Assertion (A): Bulk modulus of elasticity \(B\) represents the incompressibility of the material.
Reason (R): \( B=-\frac{\Delta p}{\Delta V / V} \), where symbols have their usual meaning.
 
1. Both (A) and (R) are true and (R) is the correct explanation of (A).
2. Both (A) and (R) are true but (R) is not the correct explanation of (A).
3. (A) is true but (R) is false.
4. (A) is false but (R) is true.
 
Subtopic:  Shear and bulk modulus |
 51%
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