← Legal Metrology
Past Questions
In the case of stream line flow, the loss of energy is
A)
minimum
B)
maximum
C)
zero
D)
None of the above
In fluid dynamics, 'streamline flow' (also known as laminar flow in an ideal fluid context) is often analyzed under the assumption of an 'ideal fluid'. An ideal fluid is defined as being inviscid (zero viscosity) and incompressible. In such a flow, there are no shear stresses between fluid layers, meaning there is no internal friction. Since energy loss in a flowing fluid is primarily caused by viscosity (which converts kinetic energy into heat), a theoretical streamline flow of an ideal fluid results in zero energy loss. This is the fundamental assumption required to apply Bernoulli's Equation, which states that the total energy (pressure energy, kinetic energy, and potential energy) remains constant along a streamline. While real fluids always have some viscosity, in the context of standard competitive exam questions on 'streamline flow' without further qualification, it refers to the ideal case where energy loss is zero.
The gravity is measured in
A)
N
B)
kg
C)
N Kg-1
D)
NKg-2m-2
In the context of physics and gravitation, 'gravity' (specifically gravitational field strength, g) refers to the gravitational force acting per unit mass.
1. Formula: Gravitational field strength (g) = Force (F) / Mass (m).
2. Units: The SI unit of Force (F) is the Newton (N), and the SI unit of Mass (m) is the kilogram (kg).
3. Therefore, the unit for gravity/gravitational field strength is Newtons per kilogram, written as N/kg or N kg⁻¹.
Analysis of other options:
- Option (a) N: This is the unit of Force, not gravity.
- Option (b) kg: This is the unit of Mass.
- Option (d) NKg-2m-2: This is not a standard unit for gravitational field strength (it resembles the units for the Universal Gravitational Constant G, which is N m² kg⁻²).
Note: While gravity is often expressed as acceleration (m/s²), N kg⁻¹ is dimensionally equivalent to m/s² because 1 N = 1 kg·m/s², so 1 N/kg = 1 m/s².
A single slit diffraction pattern is obtained using a beam of red light. What happens, if the red light is replaced by blue light?
A)
There is no change in the diffraction pattern
B)
Diffraction fringes become narrow and crowded together
C)
Diffraction fringes become broader and farther apart
D)
Diffraction pattern disappears
In a single slit diffraction experiment, the position of the minima (dark fringes) is given by the formula: a sin(θ) = nλ, where 'a' is the slit width, 'θ' is the angle of diffraction, 'n' is the order of the minimum, and 'λ' is the wavelength of the light used. For small angles, sin(θ) ≈ θ, so θ = nλ/a. This shows that the angular width of the diffraction pattern is directly proportional to the wavelength (λ). Red light has a longer wavelength (approximately 620-750 nm) compared to blue light (approximately 450-495 nm). When red light is replaced by blue light, the wavelength λ decreases. Consequently, the angle θ decreases, meaning the fringes move closer to the central maximum. This results in the diffraction fringes becoming narrower and more crowded together. Option (c) is incorrect because it describes what would happen if the wavelength increased. Option (a) is incorrect because diffraction is wavelength-dependent. Option (d) is incorrect because diffraction occurs for all visible light wavelengths provided the slit is narrow enough.
A telescope is on the moon. If a tiny drop of ink falls on its objective, then
A)
moon will appear black
B)
field of view will be dark
C)
there will be a dark spot in the field of view
D)
brightness of the image will be slightly reduced
To understand this, we must consider how a telescope forms an image. The objective lens (or mirror) collects light from a distant object. Every point on the object sends a cone of light rays that hits the entire surface of the objective lens. All these rays are then refracted/reflected to converge at a single point in the image plane.
1. If a tiny drop of ink falls on the objective, it blocks only a small fraction of the light rays coming from every point of the observed object.
2. Since the image of any single point is formed by the integration of light from the entire aperture of the objective, blocking a small part of that aperture does not 'block' the image of a specific part of the object. Instead, it slightly reduces the total amount of light reaching the focal point for every part of the image.
3. Consequently, the entire image becomes slightly dimmer (reduced brightness), but no specific 'dark spot' appears in the field of view because the remaining clear parts of the lens still collect light from the area behind the ink drop.
Why other options are incorrect:
- Option (a): The moon is where the telescope is located; the telescope is looking at other objects, not the moon itself.
- Option (b): The field of view remains visible; it does not go completely dark unless the entire lens is covered.
- Option (c): A dark spot would only appear if the ink were placed at the focal plane (the eyepiece or the sensor), not on the objective lens. On the objective, it acts as a small stop, affecting intensity rather than geometry.
The air of the atmosphere becomes cold at higher altitudes, because of
A)
decrease in density
B)
expansion of the air
C)
variation in pressure
D)
the height above the surface of earth
The phenomenon where air temperature decreases with increasing altitude is primarily due to adiabatic cooling. As a parcel of air rises in the atmosphere, it moves from a region of higher pressure (near the surface) to a region of lower pressure. According to the laws of thermodynamics, when a gas expands against external pressure without exchanging heat with its surroundings (an adiabatic process), it must perform work. This work is done at the expense of the internal energy of the gas. Since internal energy is directly proportional to temperature, the temperature of the air parcel drops as it expands.
Analysis of other options:
- (a) Decrease in density: While density does decrease with altitude, it is a result of the pressure drop, not the direct cause of the cooling.
- (c) Variation in pressure: Pressure variation is the trigger, but the actual cooling mechanism is the 'expansion' (the process of moving from high to low pressure).
- (d) Height above the surface: Height is the location, not the physical mechanism causing the temperature change.
Theory of relativity shows that Newtonian mechanics is true
A)
approximately for all velocities
B)
approximately for low velocities
C)
approximately for high velocities
D)
wholly
The Special Theory of Relativity, proposed by Albert Einstein, generalizes the laws of physics to include objects moving at speeds close to the speed of light (c). According to relativity, the Lorentz factor γ = 1 / sqrt(1 - v²/c²) determines the magnitude of relativistic effects such as time dilation and length contraction. When the velocity (v) is very small compared to the speed of light (v << c), the term v²/c² becomes negligible (approximately 0), and γ becomes approximately 1. In this limit, the relativistic equations reduce exactly to the classical equations of Newtonian mechanics. Therefore, Newtonian mechanics is not 'wholly' true (as it fails at high speeds) nor is it true for high velocities; it serves as a highly accurate approximation for the 'low velocity' regime encountered in everyday human experience.
The lift in an aero plane is based on
A)
law of gravitation
B)
theorem of continuity
C)
Pascal’s law
D)
Bernoulli’s theorem
The lift of an airplane is primarily explained by Bernoulli's theorem, which states that for an inviscid fluid, an increase in the speed of the fluid occurs simultaneously with a decrease in pressure. An airplane wing (airfoil) is shaped such that the air traveling over the curved top surface must move faster than the air moving across the flatter bottom surface. According to Bernoulli's principle, the higher velocity on top creates a region of lower pressure, while the slower velocity on the bottom maintains a higher pressure. This pressure difference results in a net upward force called 'lift'.
Why other options are incorrect:
- a. Law of Gravitation: This describes the attractive force between masses; it is the force that lift must overcome, not the cause of lift.
- b. Theorem of Continuity: This relates to the conservation of mass (flow rate) in a pipe or stream; while it explains why air speeds up in certain areas, it does not explain the resulting pressure change that creates lift.
- c. Pascal’s Law: This relates to the transmission of fluid pressure applied to an enclosed fluid; it is used in hydraulic systems, not aerodynamics.
Ultrasonic waves are used for stirring liquid solutions, because
A)
they do not produce noise during the operation
B)
they are easy to produce
C)
they can produce perfectly homogeneous solutions
D)
they do not produce chemical reaction in the solution
Ultrasonic waves (sound waves with frequencies higher than the upper audible limit of human hearing, typically > 20 kHz) are used for stirring and mixing liquids through a process called 'Ultrasonic Homogenization' or 'Sonication'.
1. **Mechanism (Acoustic Cavitation):** When ultrasonic waves pass through a liquid, they create alternating regions of high pressure (compression) and low pressure (rarefaction). During the low-pressure cycle, tiny vacuum bubbles or cavities are formed. When these bubbles collapse violently during the high-pressure cycle, they release intense local energy and create powerful micro-jets and shock waves.
2. **Effect on Solutions:** This process breaks down particles, droplets, and aggregates into extremely small sizes (nanoscale) and distributes them uniformly throughout the liquid. This results in a perfectly homogeneous solution or emulsion that is far more stable and uniform than what can be achieved with mechanical stirring.
**Analysis of other options:**
- **Option a:** While they are inaudible to humans, the process of cavitation can produce audible noise (sub-harmonics) and the lack of noise is not the primary scientific reason for their use in stirring.
- **Option b:** Producing high-frequency ultrasonic waves requires specialized piezoelectric transducers; they are not necessarily 'easier' to produce than standard mechanical stirring.
- **Option d:** In some cases, sonication can actually trigger chemical reactions (sonochemistry) due to the extreme local temperatures and pressures created during cavitation, so this statement is not universally true nor the reason for their use in stirring.
In which process, the PV-diagram is a straight line parallel to volume axis?
A)
Isothermal
B)
Isobaric
C)
Irreversible
D)
Adiabatic
In a PV-diagram, the vertical axis (y-axis) represents Pressure (P) and the horizontal axis (x-axis) represents Volume (V). A straight line parallel to the volume axis implies that as the volume changes, the pressure remains constant. A process occurring at constant pressure is defined as an 'Isobaric' process.
Analysis of other options:
- Isothermal: For an ideal gas, PV = constant. The PV-diagram is a hyperbola, not a straight line.
- Adiabatic: For an adiabatic process, PV^γ = constant. This is also a curve (steeper than an isothermal curve), not a straight line parallel to an axis.
- Irreversible: This describes the nature of the process (non-equilibrium) rather than a specific path on a PV-diagram; it is often represented as a dashed line or a sudden jump, but it is not defined by being parallel to the volume axis.
Avogadro number is the number of molecules in
A)
one litre of gas at N.T.P
B)
one mole of a gas
C)
one gram of a gas
D)
one kilogram of a gas
Avogadro's number (denoted as Nₐ) is a fundamental constant in chemistry and physics. It is defined as the number of constituent particles (usually atoms or molecules) contained in one mole of a substance. The value is approximately 6.022 × 10²³ particles per mole.
Analysis of options:
- Option (a): One litre of gas at N.T.P. does not contain Avogadro's number of molecules. According to the molar volume of an ideal gas, one mole of gas at N.T.P. occupies approximately 22.4 litres. Therefore, one litre contains only 1/22.4 of Avogadro's number.
- Option (b): This is the correct definition. One mole of any substance contains exactly Avogadro's number of particles.
- Option (c) and (d): The number of molecules in one gram or one kilogram depends on the molar mass of the specific gas. For example, one gram of Hydrogen (H₂) contains far more molecules than one gram of Oxygen (O₂). Only the 'mole' provides a constant number of particles regardless of the substance's mass.
Two sound waves having a phase difference of 60º have path difference
A)
2λ
B)
λ/2
C)
λ/6
D)
λ/3
To find the path difference between two sound waves given their phase difference, we use the fundamental relationship between phase difference (φ) and path difference (Δx):
1. The formula relating phase difference and path difference is:
φ = (2π / λ) * Δx
where φ is the phase difference in radians, λ is the wavelength, and Δx is the path difference.
2. First, convert the given phase difference from degrees to radians:
φ = 60º
Since 180º = π radians,
φ = 60 * (π / 180) = π/3 radians.
3. Substitute the value of φ into the formula to solve for Δx:
π/3 = (2π / λ) * Δx
4. Rearrange the equation to isolate Δx:
Δx = (π/3) * (λ / 2π)
Δx = λ / (3 * 2)
Δx = λ/6
Therefore, a phase difference of 60º corresponds to a path difference of λ/6.
Comparing this to the options:
- Option a (2λ) corresponds to a phase difference of 4π (720º).
- Option b (λ/2) corresponds to a phase difference of π (180º).
- Option d (λ/3) corresponds to a phase difference of 2π/3 (120º).
Lorentz transformation holds for
A)
non-relativistic velocities only
B)
relativistic velocities only
C)
relativistic and non-relativistic velocities
D)
photons only
The Lorentz transformation is a set of mathematical equations used to relate the space and time coordinates of two observers moving at a constant velocity relative to each other.
1. **Relativistic Velocities:** The Lorentz transformation was specifically developed by Hendrik Lorentz and Albert Einstein to address the inconsistencies between Maxwell's equations of electromagnetism and Newtonian mechanics at high speeds (velocities approaching the speed of light, 'c'). It is essential for calculating time dilation and length contraction at these speeds.
2. **Non-Relativistic Velocities:** At low velocities (v << c), the Lorentz factor γ = 1 / sqrt(1 - v²/c²) approximately equals 1. When this is substituted into the Lorentz transformation equations, they simplify mathematically to the Galilean transformations (the standard transformations used in classical Newtonian physics).
Because the Galilean transformation is simply a limiting case (a special approximation) of the Lorentz transformation, the Lorentz transformation is the more general and universal law. Therefore, it holds true for all velocities, whether they are relativistic or non-relativistic.
- Option (a) is incorrect because it is too restrictive; it holds for high speeds too.
- Option (b) is incorrect because it also holds for low speeds.
- Option (d) is incorrect because while it applies to the frames observing photons, it is a general coordinate transformation for any inertial frame, not just for photons themselves.
Generally the mass of a fly wheel is concentrated on its rim. Why?
A)
To increase the moment of inertia
B)
To decrease the moment of inertia
C)
To obtain stable equilibrium
D)
To obtain a strong wheel
A flywheel is a mechanical device used to store rotational kinetic energy. The energy stored in a rotating body is given by the formula E = (1/2) Iω², where 'I' is the moment of inertia and 'ω' is the angular velocity. The moment of inertia (I) for a mass distribution is defined as the sum of the mass elements multiplied by the square of their distance from the axis of rotation (I = Σ mr²). By concentrating the mass of the flywheel on its rim (maximizing the distance 'r' from the axis), the moment of inertia is significantly increased. A higher moment of inertia allows the flywheel to resist changes in its rotational speed, thereby smoothing out fluctuations in energy supply or demand and maintaining a more constant angular velocity.
Option (b) is incorrect because decreasing the moment of inertia would make the wheel easier to stop or speed up, defeating the purpose of an energy reservoir. Options (c) and (d) are irrelevant to the primary physical function of a flywheel's mass distribution.
The equation of state for n moles of an ideal gas is PV=nRT, where R is a constant. The S.I. unit for R is
A)
J K-1 per molecules
B)
J Kg-1K-1
C)
J K-1 mol-1
D)
J K-1g-1
To find the S.I. unit of the universal gas constant R, we rearrange the ideal gas equation PV = nRT to solve for R: R = PV / (nT). Now, we substitute the S.I. units for each variable:
1. P (Pressure) is measured in Pascals (Pa), where 1 Pa = 1 N/m².
2. V (Volume) is measured in cubic meters (m³).
3. n (Amount of substance) is measured in moles (mol).
4. T (Temperature) is measured in Kelvin (K).
Substituting these into the formula:
Unit of R = (Pa * m³) / (mol * K)
Since Pa = N/m², the unit becomes:
Unit of R = ((N/m²) * m³) / (mol * K) = (N * m) / (mol * K).
Since 1 Newton-meter (N*m) is equal to 1 Joule (J), the unit simplifies to:
Unit of R = J / (mol * K) or J mol⁻¹ K⁻¹ (which is equivalent to J K⁻¹ mol⁻¹).
Comparing this to the options:
- Option (a) refers to the Boltzmann constant (k), not the universal gas constant R.
- Option (b) and (d) use mass (Kg or g) instead of moles, which would be the unit for the specific gas constant (R_specific = R/M), not the universal gas constant R.
A rocket is fired from the earth to the moon. The distance between the earth and the moon is r and the mass of the earth is 81 times the mass of the moon. The gravitational force on the rocket will be zero, when its distance from the moon is
A)
r/20
B)
r/15
C)
r/10
D)
r/5
To find the point where the gravitational force on the rocket is zero, the gravitational pull from the Earth must be equal and opposite to the gravitational pull from the Moon.
1. Let $M_e$ be the mass of the Earth and $M_m$ be the mass of the Moon.
2. Given: $M_e = 81 M_m$.
3. Let $r$ be the total distance between the Earth and the Moon.
4. Let $x$ be the distance of the rocket from the Moon. Therefore, the distance of the rocket from the Earth is $(r - x)$.
5. At the point where the net force is zero:
$F_{earth} = F_{moon}$
$rac{G M_e m}{(r - x)^2} = rac{G M_m m}{x^2}$
6. Simplifying the equation by canceling $G$ and $m$ (mass of the rocket):
$rac{M_e}{(r - x)^2} = rac{M_m}{x^2}$
7. Substitute $M_e = 81 M_m$:
$rac{81 M_m}{(r - x)^2} = rac{M_m}{x^2}$
$rac{81}{(r - x)^2} = rac{1}{x^2}$
8. Taking the square root of both sides:
$rac{9}{r - x} = rac{1}{x}$
9. Solving for $x$:
$9x = r - x$
$10x = r$
$x = r/10$
Thus, the gravitational force on the rocket will be zero when its distance from the moon is $r/10$.
In nodular iron, graphite is in the form of
A)
cementite
B)
free carbon
C)
flakes
D)
spheroids
Nodular iron, also known as ductile iron, is a type of cast iron where the graphite exists as spherical nodules (spheroids) rather than flakes. This is achieved by adding a nodulizing agent, typically magnesium or cerium, to the molten metal before casting. The spherical shape of the graphite minimizes stress concentrations within the metal matrix, which significantly improves the material's ductility, toughness, and tensile strength compared to grey cast iron.
Analysis of other options:
- a. Cementite: This is a hard, brittle intermetallic compound (Fe3C) found in white cast iron, not the form of graphite in nodular iron.
- b. Free carbon: While graphite is a form of free carbon, this term is too general and does not describe the specific morphology (shape) characteristic of nodular iron.
- c. Flakes: Graphite in the form of flakes is the defining characteristic of Grey Cast Iron, which makes the material brittle.
Twisting couple in a shaft introduces in it
A)
bending moment
B)
deflection
C)
shear stress
D)
shean strain
When a twisting couple (torque) is applied to a shaft, it creates a state of torsion. In torsion, the internal resistance of the material manifests as shear stress. This stress acts on planes perpendicular to the longitudinal axis of the shaft and also on the cross-sectional plane. According to the torsion formula (T/J = τ/r = Gθ/L), the shear stress (τ) is directly proportional to the applied torque (T).
Why other options are incorrect:
- a. Bending moment: This is caused by transverse loads (forces acting perpendicular to the axis), not by a twisting couple.
- b. Deflection: While torsion causes an angular twist (rotation), 'deflection' typically refers to the linear displacement caused by bending.
- d. shean strain: This appears to be a typographical error for 'shear strain'. While shear strain does occur, the primary 'introduction' or effect of the twisting couple on the material's internal resistance is the development of shear stress. In the context of standard Strength of Materials examinations, 'shear stress' is the primary answer for the effect of torque.
The value of moment of inertia for a solid shaft of diameter d is equal to
A)
πd4/32
B)
πd4/64
C)
πd4/16
D)
πd4/48
In the context of Strength of Materials, the 'moment of inertia' for a solid circular shaft usually refers to the Area Moment of Inertia (also known as the Second Moment of Area) about its centroidal axis, which is critical for calculating bending stress.
1. The formula for the Area Moment of Inertia (I) of a circle with radius 'r' is I = (πr^4)/4.
2. Since the diameter 'd' is twice the radius (d = 2r), we substitute r = d/2 into the formula:
I = (π * (d/2)^4) / 4
I = (π * (d^4 / 16)) / 4
I = πd^4 / 64.
Comparison with other options:
- Option (a) πd^4/32 is the Polar Moment of Inertia (J), which is used for calculating torsional shear stress (J = 2I).
- Option (c) and (d) are mathematically incorrect for a standard solid circular cross-section.
The maximum principal stress theory is applicable for
A)
ductile material
B)
brittle material
C)
elastic material
D)
none of them
The Maximum Principal Stress Theory, also known as Rankine's Theory, states that failure occurs when the maximum principal stress in a complex stress system reaches the yield stress (or ultimate stress) of the material in a simple tension test.
1. **Brittle Materials**: Brittle materials (like cast iron or stone) typically fail due to sudden fracture when the normal stress reaches a critical limit, without significant plastic deformation. Rankine's theory aligns well with this failure mode, making it the most suitable theory for brittle materials.
2. **Ductile Materials**: Ductile materials (like mild steel) usually fail due to shear (sliding of planes). Therefore, theories based on shear stress, such as the Maximum Shear Stress Theory (Tresca) or the Maximum Distortion Energy Theory (von Mises), are used for ductile materials.
3. **Elastic Material**: While the theory is applied within the elastic limit, 'elastic' is a general property of both brittle and ductile materials; it is not the specific category of material for which this failure theory is uniquely applicable.
Therefore, the Maximum Principal Stress Theory is specifically applicable to brittle materials.
Idler pully is used for
A)
changing the direction of motion of the belt
B)
applying tension
C)
increasing velocity ratio
D)
none of them
An idler pulley is a pulley that does not transmit power but is used for specific mechanical purposes in a belt drive system. Its primary functions are: 1) To maintain proper tension in the belt to prevent slippage (acting as a tensioner), and 2) To increase the angle of wrap (arc of contact) on the driving or driven pulley to improve grip and power transmission. While an idler can technically change the direction of a belt, its fundamental engineering purpose in the context of belt drive efficiency is to ensure the belt remains taut (applying tension). Option (a) is a secondary effect, but (b) is the primary functional purpose. Option (c) is incorrect because the velocity ratio is determined by the diameters of the driving and driven pulleys, not by the idler pulley.
Pipes for bicycle frames are made of
A)
cold rolled steel
B)
hot rolled steel
C)
forged steel
D)
cast steel
Bicycle frames require a combination of high strength, lightweight properties, and precise dimensional tolerances. Cold rolled steel is the correct choice because: 1. Strength: Cold working (rolling steel at room temperature) increases the yield strength of the material through a process called strain hardening or work hardening. 2. Surface Finish: Cold rolling produces a much smoother surface finish and tighter dimensional tolerances compared to hot rolling, which is essential for the thin-walled tubing used in bicycle frames. 3. Weight: Because cold rolled steel is stronger, thinner walls can be used to achieve the necessary structural integrity, thereby reducing the overall weight of the frame. In contrast, hot rolled steel (Option b) is typically used for structural beams where precision and high strength-to-weight ratios are less critical. Forged steel (Option c) is used for components like cranks or bottom brackets, not for long pipes. Cast steel (Option d) is too brittle and lacks the structural properties required for a bicycle frame.
Which of the following is the binding material in cemented carbides
A)
cobalt
B)
nickel
C)
vanadium
D)
carbon
Cemented carbides (also known as tungsten carbide) are composite materials consisting of hard ceramic particles (typically Tungsten Carbide, WC) bonded together by a metallic binder. Cobalt (Co) is the most widely used binding material because it has excellent wetting properties with tungsten carbide, allowing it to flow around the hard particles during the liquid-phase sintering process, creating a dense, strong, and tough composite.
Why other options are incorrect:
- Nickel (b): While nickel can be used as a binder (especially for improved corrosion resistance), cobalt is the standard and primary binding material for general-purpose cemented carbides.
- Vanadium (c): Vanadium is often added in small quantities as a grain growth inhibitor to maintain a fine microstructure, but it does not act as the primary binding matrix.
- Carbon (d): Carbon is a constituent of the carbide phase itself (e.g., WC), not the metallic binder that holds the carbide grains together.
The following is the inversion of slider crank chain mechanism
A)
Whitworth quick return mechanism
B)
Hand pump
C)
Oscillating cylinder engine
D)
All of them
A slider-crank chain consists of three turning pairs and one sliding pair. An inversion is obtained by fixing different links of the kinematic chain.
1. **Whitworth quick return mechanism**: This is an inversion of the slider-crank chain where the crank is fixed (or a specific link arrangement is used to create a quick return motion), allowing the slider to move in a straight line while the tool oscillates.
2. **Hand pump**: In a hand pump, the cylinder (the sliding part's guide) is fixed. This is a classic inversion of the slider-crank mechanism where the frame/cylinder is the fixed link.
3. **Oscillating cylinder engine**: In this mechanism, the crank is fixed, and the cylinder itself is allowed to oscillate. This is another recognized inversion of the slider-crank chain.
Since all three listed mechanisms are derived from the inversion of the slider-crank chain, the correct option is 'All of them'.
Guest’s theory of failure is applicable for the following type of materials
A)
brittle
B)
ductile
C)
elastic
D)
plastic
Guest's theory of failure, also known as the Maximum Shear Stress Theory (MSS Theory) or Tresca's Criterion, states that failure occurs when the maximum shear stress in a material reaches the shear stress at the yield point in a simple tension test. This theory is specifically designed for ductile materials because ductile materials typically fail by sliding along slip planes (shear failure) rather than by sudden fracture (normal stress failure).
Comparison with other options:
- Brittle materials (Option a) are better described by the Maximum Principal Stress Theory (Rankine's Theory) because they fail due to normal stress (cleavage).
- Elastic (Option c) and Plastic (Option d) refer to the behavior of the material under load rather than the category of material for which the failure criterion is defined. While ductile materials exhibit plastic deformation, the theory is categorized as being applicable to 'ductile' materials.
The materials having same elastic properties in all directions are called
A)
ideal materials
B)
isotropic materials
C)
elastic materials
D)
uniform materials
In the study of Strength of Materials, materials are classified based on their properties relative to direction and location:
1. **Isotropic Materials**: These are materials whose mechanical properties (such as Young's modulus, Poisson's ratio, and shear modulus) are identical in all directions at any given point. For example, most metals (like steel) are considered isotropic.
2. **Anisotropic Materials**: These are materials whose properties vary depending on the direction of the applied load. Wood is a classic example, as it is stronger along the grain than across it.
3. **Homogeneous Materials**: These are materials that have the same properties at all points throughout the body, regardless of location (though they may still be anisotropic).
Analyzing the options:
- **Option a (Ideal materials)**: This is a general term and not a technical classification for directional properties.
- **Option b (Isotropic materials)**: Correct. By definition, 'iso' means same and 'tropos' means direction.
- **Option c (Elastic materials)**: This refers to the ability of a material to return to its original shape after the removal of a load, regardless of whether the properties are the same in all directions.
- **Option d (Uniform materials)**: This is often used interchangeably with 'homogeneous,' referring to consistency in composition throughout the volume, not necessarily the direction of properties.