Physics Mechanical Properties of Matter

Question 1

Give the dimensional formula of Stress

Answer 1

The dimensional formula of stress is ML^-1T^-2

Question 2

Define Longitudinal Strain

Answer 2

Longitudinal Strain or Tensile Strain is defined as the ratio of change in length to the original length of the body.
Longitudinal Stress is given by ΔL/L

Question 3

Define Shearing or shear strain

Answer 3

Shear Strain is defined as angular deformation produced under the action of tangential forces.

Question 4

Define Volumetric Strain

Answer 4

Volumetric Strain is defined as the change in volume per unit original volume of a body without any change in its shape.
Volumetric Strain = ΔV/V

Question 5

Draw the graph of the behaviour of a wire under increasing load and also explain it explicitly

Answer 5

Consult the book, bhai.

Question 6

Give the 3 types of Modulus of Elasticity corresponding to the strain

Answer 6

The 3 types of the modulus of elasticity corresponding to strain are as follows:

(i) Corresponding to Longitudinal Strain, we have Young’s Modulus
(ii) Corresponding to Volume Strain, we have Bulk Modulus
(iii) Corresponding to Shear Strain, we have Modulus of Rigidity

Question 7

Define Young’s Modulus

Answer 7

Young’s Modulus is defined as the ratio of longitudinal stress to the corresponding strain produced, within elastic limits.

Question 8

Give the Formula of Young’s Modulus

Answer 8

Stress = F/A
Strain = l/L
Now, Young’s Modulus = Tensile Stress / Tensile Strain
= (F/A) / (l/L) = FL/Al
This relation holds good for compressive as well as extensive stress. Since strain has no unit being a ratio, hence Young’s Modulus has the same unit as stress i.e N/m²

Question 9

Give the formula of Bulk’s Modulus

Answer 9

K = P/(-v/V) = -PV/v
The negative sign indicates that by an increase in pressure a decrease in volume occurs
The only stress which a liquid or a gas can permanently sustain is hydrostatic pressure. Hence, the Bulk Modulus is the only elastic modulus that can be experienced by liquids i.e Hydrostatic Pressure. It has the same unit as pressure

Question 10

Whats Compressibility?

Answer 10

The reciprocal of bulk modulus of a substance is called Compressibility.
Compressibility = 1/K = -(v/V)/P

Question 11

Define Poisson’s Ratio

Answer 11

Within elastic limit, there is a complete proportionality between the lateral strain and longitudinal strain, the ratio of lateral strain and longitudinal strain is constant for a material of a body which is called Poisson’s Ratio.

Question 12

Derive the Poisson’s Ratio

Answer 12

Let us consider a rod has its original diameter and length as D and L, respectively and, if an increase in length due to a given longitudinal force is l and reduction in diameter is d, then Poisson’s ratio is given as
σ = (d/D)/(l/L) = (Ld)/(lD)
or
σ = (L/D) dD/dL

Question 13

Give the two equations equating the 4 elastic constants

γ, K, η, and η

Answer 13

The two equations are as follows:
γ = (9ηK) / (3K+η)

and

σ = (3K-2η) / (6K+2η)

Question 14

Prove that Shearing Shearing Stress is equivalent to an equal Linear Tensile Stress and equal Compressive Stress at right angles to each other

Answer 14

Consult the book,bhai.

Question 15

Derive the relation between γ, K and σ

Answer 15

Consult the book, bhai.

Question 16

Derive the relation between γ, η and α

Answer 16

Consult the book, bhai.

Question 17

Derive the relation between Y, K and η

Answer 17

Consult the book, bhai.

Question 18

Derive the relation between K, η and σ

Answer 18

Consult the book, bhai.

Question 19

Give the limiting values of Poisson’s Ratio

Answer 19

We know, 3K(1-2σ) = 2η( 1 + σ)
Since K and η are essentially positive quantities , hence
1. If Poisson’s ratio (σ) is a positive quantity , the both sides of the above equation must be positive, which is possible only when (1-2σ) > 0 ⇒ σ<1/2 or 0.5
2. If Poisson’s ratio(σ) is a negative quantity then the left side of the equation will be positive, It means right hand should also be positive which is possible only when
(1+σ)>0 or σ>-1
Hence, the theoretical value of σ lies between -1 and 0.5 ie -1

Question 20

Define Torsional Pendulum

Answer 20

Draw the diagram and describe it a little bit.

Question 21

Give the two uses of Tortional Pendulum

Answer 21

The Two uses of Torsional Pendulum are as follows:

(i) Determination of Moment of Inertia of an irregular body
(ii) Determination of Tortional Rigidity

Question 22

Explain using derivation how the moment of inertia of an irregular body is found out

Answer 22

Consult the book, bhai.

Question 23

Explain using derivation how the Torsional Rigidity is found out

Answer 23

Consult the book, bhai.

Question 24

Define a beam

Answer 24

A beam is defined as a rod or bar of uniform rectangular or circular cross-section whose length is very large in comparison to its thickness or radius.

Question 25

Give the 4 assumptions taken when studying bending of beam

Answer 25

The 4 assumptions taken when studying bending of a beam are as follows:

(i) In comparison to the load( what they can support), their weight is negligible
(ii) Shearing forces are negligible
(iii) Geometrical moment of Inertia of a beam remains the same which means the cross-section of a beam remains unaltered.
(iv) The curvature of the beam is small.

Question 26

Define a cantilever along with its diagram

Answer 26

Consult the book bhai.

Question 27

How is Young’s Modulus determined by bending of beam?

Answer 27

Consult the book bhai

Question 28

Give the formula using which a Torsion pendulum is used to determine the moment of inertia of an irregular body

Answer 28

I2 = I1 x (T²2-T²)/(T²1-T²)