Elastic behaviour of solids MCQ Quiz in मल्याळम - Objective Question with Answer for Elastic behaviour of solids - സൗജന്യ PDF ഡൗൺലോഡ് ചെയ്യുക

Concept:

Young’s modulus: 

• Young's modulus a modulus of elasticity, applicable to the stretching of wire, etc., equal to the ratio of the applied load per unit area of the cross-section to the increase in length per unit length.
• It is denoted as E or Y.
• The unit of Young’s modulus is N m-2.

\(\text{Y}=\frac{\text{ }\!\!σ\!\!\text{ }}{\epsilon }\)

Where σ = stress, ϵ = strain in wire.

• Young’s Modulus Formula by using other quantities:

\({\rm{Y}} = \frac{{{\rm{F}}{{\rm{L}}_0}}}{{{\rm{A\Delta L}}}}\)

Where F = force exerted under tension, A = actual cross-sectional area, L0 = actual length, ΔL = change in length.

Calculation:

Given, 

Actual length of wire L₀ = 1 m

Actual cross sectional area A = 1 cm² = 10 ^-4 m²

ΔL = change in length = 1 mm = 10 ^-3 m

Youngs modulus Y = 1011 N/m2

Force required F

Now, using these parameters in the formula of Youngs Modulus. 

\(\)\(10^{11} = \frac{F(1)}{10^{-4}10^{-3}}\)

\(\implies 10^{11} = \frac{F(1)}{10^{-7}}\)

⇒ F = 10¹¹ × 10 ^-7 = 10⁴ N

So, the correct option is 104 N

Concept:

Modulus of elasticity is also a measure of a material's stiffness or resistance to elastic deformation.

Elasticity is a property of an object or material indicating how it will restore it to its original shape after distortion.

A higher value of the Young modulus of metal indicates higher stiffness.

CONCEPT:

• Elastic behaviour of solids: An attribute of rigid bodies to restore their original shape and is called elastic behaviour.
  • Each molecule in the elastic solids is acted upon by the forces because of neighboring molecules.
  • These forces are called intermolecular forces.
  • The elastic behavior of solids can be explained by observing the intermolecular forces of these microscopic nature of the solids.
  • When a solid body is deformed, the molecules inside it are displaced from their equilibrium positions (fixed points of lattice points) causing a change in intermolecular and interatomic distances.
  • When this external force is removed, the interatomic force between the molecules tries to bring back the body into its original position.
  • Thus, the body comes to its original shape again.

EXPLANATION:

• Atoms in the solid can be taken as the ball in the spring ball model.
• The intermolecular force between the molecules of the solid can be taken as spring force in the spring ball model.
• When there will be an external force, the balls (molecules) will be displaced and the length of the spring will be increase or decrease.
• Hence a force will generate that will tend to make balls (molecules of the solid) back to the original position.
• So spring ball system can be used to understand the molecular phenomenon of the elastic solids.
• Hence the correct answer is option 2.

CONCEPT:

• Elastic behaviour of solids: An attribute of rigid bodies to restore its original shape and is called elastic behaviour.

• Each molecule in the elastic solids is acted upon by the forces because of neighboring molecules.
• These forces are called intermolecular forces.
• The elastic behavior of solids can be explained by observing the intermolecular forces of these microscopic nature of the solids.
• When a solid body is deformed, the molecules inside it are displaced from their equilibrium positions (fixed points or lattice points) causing a change in intermolecular and interatomic distances.
• When this external force is removed, the interatomic force between the molecules tries to bring back the body into its original position.
• Thus, the body comes to its original shape again.

EXPLANATION:

• Each molecule of an elastic solid is acted upon by the forces because of neighboring known as intermolecular force.
• Due to an external force on an elastic body, the body gets displaced.
• Hence molecules are displaced from their original position.
• But when the external force is removed, they come back to its original position.
• Hence the force between the molecules (intermolecular forces) is in stable equilibrium.
• So the correct answer is option 1.

​
Additional Information

• Equilibrium: It is a state where the resultant of all forces acting on a body is zero.

Equilibrium is of mainly three types:

Stable equilibrium	Unstable equilibrium	Neutral equilibrium
A system is said to be in stable equilibrium if, when displaced from equilibrium, it experiences a net force or torque in a direction opposite the direction of the displacement	A system is in unstable equilibrium if, when displaced from equilibrium, it experiences a net force or torque in the same direction as the displacement from equilibrium.	A system is in neutral equilibrium if its equilibrium is independent of displacements from its original position.
The potential energy is minimum in this case.	The potential energy is maximum in this case.	The potential energy remains constant in this case.

Concept:

Hooke's Law: For an elastic spring, the force (tension) F is proportional to the extension (or compression) from its natural length 

F = K(L-l)

where:
F is the tension in the spring,
L is the length of the spring under tension,(L-l)  is the natural (unstretched) length of the spring, k is the spring constant.

Calculation:

Here, 3 = K (a – ℓ) and 2 = K (b – ℓ)

⇒T = K (3a – 2b – ℓ)

⇒T = K (3(a – ℓ) – 2 (b – ℓ)

\(=\mathrm{K}\left[3\left(\frac{3}{\mathrm{~K}}\right)-2\left(\frac{2}{\mathrm{~K}}\right)\right] \)

⇒9 - 4

⇒5 N

For its length (3a – 2b), the value of tension will be 5 N.

Correct option-3

Concept:

According to Hooke’s law,
“For small deformation, the stress in a body is proportional to the corresponding strain.”

i.e. stress  ∝ strain 
or stress = (E) (strain)
Here, E is a constant called the modulus of elasticity.
Now, depending upon the nature of the deforming force applied on the body, stress, strain, and

hence modulus of elasticity are classified into the following three types:
1. Young's modulus
2. Bulk modulus and
3. Modulus of rigidity

Explanation:

• Hooke's law of elasticity is only valid within the elastic limit of material because-
• Beyond the elastic limit, the material is not going to regain its original shape and size after the removal of the force.
• This applied force is called deforming force while force applied by material to restore the original size is called restoring force.

​

For the given stress-strain graph E is the elastic limit of a material.

Hence, option-3 is correct

The correct answer is option 2) i.e. P2 comes to rest earlier than P1

CONCEPT:

• Elastic behaviour of solids: Elasticity is the property of solid materials to return to their original shape and size after the forces deforming acting on them have been removed. 
  • Solids are made up of molecules that are held together by intermolecular forces.
  • When an external force acts on the solid, the molecules get displaced and cause deformation.
  • Once the force ceases to act, the intermolecular forces drive the molecules back to their original position. This is how materials attain their initial shape and size.
  • The forces acting on the materials generate stress. If continuous stress is applied beyond the elastic limit of a material, the material starts deforming.
• Elastic fatigue: The temporary loss of elastic properties due to repeated deforming force acting on an object is called elastic fatigue. 
  • Elastic fatigue can occur even if the deforming forces are within the elastic limit.

EXPLANATION:

• A pendulum oscillating is subjected to a force.
• As pendulum P₂ was initially subjected to deforming force and oscillating, further oscillations will lead to elastic fatigue.
• On the other hand, pendulum P₁ was at rest. Hence, it will not be under elastic fatigue.
• If a body is subjected to stress or strain continuously it becomes weak due to elastic fatigue. Therefore, P2 comes to rest earlier than P1​

correct answer is Elasticity

Key Points

CONCEPT:

• Elasticity is the ability of a body that resists the body to distort under any force and try to return to its original shape and size when that force is removed.
• Elasticity for different substances is calculated by different experiments using Stress and strain.

Plasticity: 

The ability of a body that can not make it to its original shape and size after deformation when force is removed is called plasticity.

• It remains in its deformed position when force is removed.
• Viscosity: The state of being thick, sticky, and semi-fluid inconsistency, due to internal friction is called viscosity.
• Surface tension: The property of the liquid surfaces to shrink into the minimum surface area possible is known as surface tension.

EXPLANATION:

• Viscosity is the property of liquids, not solids. So this can't be the answer.
• Similarly, surface tension is the property of liquids, not solids. So this can't be the answer.
• The plastic property of solids can not make them return to their original shape and size.
• The ability of solids that makes them return to their original shape and size after deformation is called elasticity.

Hence the correct answer is option 3

Concept:

• Elastic potential energy is the energy stored as a result of applying a force to deform an elastic object. 
• The energy is stored until the force is removed and the object regains its original shape, doing work in the process.
• This deformation could involve compressing, stretching, or twisting the object.
• Many objects are specifically designed  to store elastic potential energy inside them,

​For example:

The coil spring of a wind-up clock

An archer's stretched bow

A stretched slingshot ready to fire.

Calculation:

Given:-

Length of wire, L = 4 cm

Stretched length, \(\Delta L=2\times 10^{3}\)

Cross-sectional area, \(A=2\times 10^{-6}m^{2}\)

Young's modulus, \(Y=2\times 10^{11}N/m^{2}\)

Now, the energy density of the stretched wire is given by-

\(U=\frac{1}{2}\times stress\times strain\)

\(U=\frac{1}{2}\times Y\times (strain)^{2}\)

⇒ \(U=\frac{1}{2}\times 2\times 10^{11}\times \left ( \frac{2\;\times\; 10^{-3}}{4} \right )^{2}\)

⇒ \( U=0.25\times 10^{5}\)

\(\therefore U=2.5\times 10^{4}J/m^{3}\)

Hence, option 1 is correct

CONCEPT:

• Plasticity is the ability of a body in which when it is distorted under any force (Stress), it has no tendency to return to its original shape and size when that force is removed.

EXPLANATION:

• A solid has a definite shape and size.
• If you want to change the shape or size of a body, you need a force.
• If you apply force to a lump of putty or mud, they get permanently deformed. Also, they have no tendency to regain their previous shape.
• This property is called plasticity and such materials are called plastic material.
• So, the ideal plastic materials are putty and mud.
• Steel is an elastic material, not plastic.
• Hence the correct answer is option 3.