Tag: properties of material substances

Questions Related to properties of material substances

When the elastic limit is exceeded, the body acquires permanent deformation called 

physics properties of material substances elastic behaviour of solids elastic and plastic substances properties of substances

  1. Met

  2. Set

  3. bet

  4. ket

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Correct Option: A

The nearest approach to a perfect plastic body is

physics properties of material substances elastic behaviour of solids elastic and plastic substances properties of substances

  1. diamond

  2. quartz fiber

  3. putty

  4. none of these

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Correct Option: B

The materials, which do not show a fixed trend of deformation vs. applied force, are called:

physics properties of material substances elastic behaviour of solids elastic and plastic substances properties of substances

  1. inelastic materials

  2. plastic materials

  3. elastic materials

  4. rigid materials

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Correct Option: A
Explanation:

Elastic materials are those that follow the Hooke's law, which is that the deformation produced in a material is directly proportional to the stress applied to it, and the material is recoverable after the deformation force is removed.

Inelastic materials are those that do not follow this relationship. They do not show a fixed trend of deformation vs applied force; in fact, they might not deform at all (rigid materials) or the deformation observed is not completely recoverable.

The elastic energy stored per unit volume in a stretched wire is

elastic energy properties of material substances elasticity properties of matter physics

  1. $\cfrac { 1 }{ 2 } \cfrac { { \left( stress \right) }^{ } }{ Y } $

  2. $\cfrac { 1 }{ 2 } \cfrac { { \left( stress \right) }^{ 2 } }{ Y } $

  3. $\cfrac { 1 }{ 2 } \cfrac { { \left( stress \right) }^{ 2 } }{ { Y }^{ 2 } } $

  4. $\cfrac { 1 }{ 2 } \cfrac { { \left( stress \right) }^{ } }{ { Y }^{ 2 } } $

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Correct Option: B
Explanation:

The elastic energy stored per unit volume in a stretched wire is
$u=\cfrac { 1 }{ 2 } \times stress\times strain=\dfrac { { (stress) }^{ 2 } }{ 2Y } \left( \because Y=\cfrac { stress }{ strain }  \right) $ 

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:

elastic energy properties of material substances elasticity properties of matter physics

  1. $\frac{S}{2Y}$

  2. $\frac{2Y}{S^2}$

  3. $\frac{S^2}{2Y}$

  4. $2S^2Y$

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Correct Option: C
Explanation:
Energy stored per unit volume can be given as: 
 $E  =\dfrac{1}{2} \times stress \times strain $ -----------(1)      
From Hooke's law :
Young's modulus, $Y = \dfrac{Stress}{Strain}$

$\implies$    $Strain   = \dfrac{Stress}{Y}   = \dfrac{S}{Y}$ -----------(2)  
  
From equation (1) and (2): 
$\therefore$    $E = \dfrac{1}{2} \times S \times \dfrac{S}{Y} $

$\Rightarrow E=  \dfrac{1}{2} \dfrac{S^2}{Y}$
Hence, the correct option is $(C)$

One end of an aluminium wire whose diameter is 2.5 mm is welded to one end of a copper diameter is 1.8 mm. The composite wire carries a steady current i of I .3 A. What is the current density in each wire ?

elastic energy properties of material substances elasticity properties of matter physics

  1. $j _{Cu}= 26 A/cm^2, j _{Al}= 51 A/cm^2$

  2. $j _{Cu}=51A/cm^2 , j _{Al}= 26A/cm^2$

  3. $j _{Cu}=40A/cm^2, j _{Al}= 60 A/cm^2$

  4. $j _{Cu}= 60 A/cm^2, j _{Al}= 40 A/cm^2$

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Correct Option: C

Two wires are of same material. Wire 1 is of 4 times longer than wire 2 and area of wire 1 is 4 times less than wire 2. Compare the stresses if they are elongated by the same load

elastic energy properties of material substances elasticity properties of matter physics

  1. 1/2

  2. 4

  3. 1/4

  4. 2

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Correct Option: C
Explanation:

The stress is given by Force/Area . 
Comparing the stresses, we get, $(stress _1/stress _2)=(L _2/L _1)=1/4$

The correct option is (c)

Two wires of different material but of same radius and length are stretched by the same load, the ratio of the stresses in the material will be same

elastic energy properties of material substances elasticity properties of matter physics

  1. True

  2. False

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Correct Option: A
Explanation:

The stress depends only on the load and the area of cross section. Thus, the stress produces will also be same

Two wires of different material but of same radius and different length are stretched by the loads in the ratio 1:3, the ratio of the stresses in the material will be same

elastic energy properties of material substances elasticity properties of matter physics

  1. 3:1

  2. 2:3

  3. 3:2

  4. 1:3

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Correct Option: D
Explanation:

The stress is directly proportional to the force applied and the inversely proportional to area of cross section. Thus as force ratio is 1:3, the stress ratio will also be 1:3

The correct option is (d)

The total strain energy stored in a body is known as 

elastic energy properties of material substances elasticity properties of matter physics

  1. Resilience

  2. Toughness

  3. Modulus of resilience

  4. None of the above

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Correct Option: A
Explanation:

The strain energy is released when the object is unloaded, which is nothing but resilience

Resilience is the ability of a material to absorb energy when deformed, and release that energy upon unloading

The correct option is (a)