Full Test 3 - EKT Mechanical - AFCAT MCQ

For given values |A − λI| = 0

⇒ (3 – λ) (– 20 + 4λ – 5λ + λ² + 18) + 2 (20 – 4λ – 12) + 2 (-12 + 8 + 2λ) = 0
⇒ λ³ – 4λ² + 5λ – 2 = 0
Only 1 and 2 satisfy this equation.
λ = 1, 1, 2
Hence, smallest Eigen value = 1 and Largest Eigen value = 2

Given that 
Squaring the above equation, we get 
Putting the values, the equation becomes 

∴ Angle between 

We know that 2sin²2t = (1 − cos4t)
Apply Laplace transform on both sides then we get,

Integrating Factor 

Let the side of the square is x
Now, the area of square is, A = x²
Given that area of the square increased by 69%, the area will be 1.69 A
Let the increased side of the square is nx

⇒ (nx)² = 1.69x²
⇒ n = 1.3
Hence the side of the square increases by 30%

Euler’s Number is defined as the square root of the ratio of the inertia force of a flowing fluid to the pressure force. Mathematically

In radioactive processes, particles or electromagnetic radiation are emitted from the nucleus. The most common forms of radiation emitted have been traditionally classified as alpha (a), beta (b), and gamma (g) radiation. Nuclear radiation occurs in other forms, including the emission of protons or neutrons or spontaneous fission of a massive nucleus.

Surface tension is the elastic tendency of a fluid surface which makes it acquire the least surface area possible. Surface tension is measured in SI units of N/m (Newton per meter). The cohesive forces among liquid molecules are responsible for the phenomenon of surface tension.

So the dimensions of surface tension are [M¹L⁰T⁻²]

RC is the time constant of a series resistance capacitance DC voltage circuit. The dimension of RC is same as that of time.

Permeance is the measure of the ease with which flux can be set up in a material. In other words, it measures the magnitude of the flux for the number of turns in an electric circuit. The permeance is analogous to the conductance in an electrical circuit. It is reciprocal of the reluctance (R) of the material in a magnetic circuit.

Lead = pitch × no of start = 4 × 2 = 8mm

The principal features of the British Standard Whitworth (BSW) thread form are that the angle between the thread flanks is 55 degrees and the thread have radii at both the roots and the crests of the thread.

The Zoom command is given by clicking the Zoom icons on the Zoom toolbar or by clicking View ≫ Zoom ≫ Zoom icons.

It can also be given by typing “Z” on the command line. Then select options like “a” for the entire drawing or grid limits or “w” for the window to enlarge a particular area and so on. Click ENTER to activate the command.

Condition for Maximum power transmitted by belt is : T = 3T_C i.e. power transmitted will be maximum when tension is equal to three time centrifugal tension or It shows that when the power transmitted is maximum, 1/3rd of the maximum tension is absorbed as centrifugal tension.

Flange coupling is a driving coupling between rotating shafts that consists of flanges (or half couplings) one of which is fixed at the end of each shaft, the two flanges being bolted together with a ring of bolts and nuts to complete the drive

Conservation of linear momentum

Resultant between two forces P and Q, acting at an angle θ is defined as:

The section modulus (Z) of the cross-sectional shape is significant in designing beams. It is a direct measure of the strength of the beam. A beam that has a larger section modulus than another will be stronger and capable of supporting greater loads.

To calculate Z, the distance (y) to the extreme fibres from the centroid (or neutral axis) must be found as that is where the maximum stress could cause failure.

Contra-flexure = contra (opposite) + flexure (bending)

In a bending beam, a point is known as a point of contra flexure if it is a location at which no bending occurs. In a bending moment diagram, it is the point at which the bending moment curve intersects with the zero line. In other words where the bending moment changes its sign from negative to positive or vice versa. It occurs in the overhanging beam.

Maximum principal stress theory (Rankine’s theory)

According to this theory, the permanent set takes place under a state of complex stress, when the value of maximum principal stress is equal to that of yield point stress as found in a simple tensile test.

For design criterion, the maximum principal stress (σ₁) must not exceed the working stress ‘σ_y’ for the material.

Note: For no shear failure τ ≤ 0.57 σ_y
Maximum principal strain theory (ST. Venant’s theory)
According to this theory, a ductile material begins to yield when the maximum principal strain reaches the strain at which yielding occurs in simple tension.

 

σ₁, σ₂ and σ₃ = Principal stresses   

Maximum shear stress theory (Guest & Tresca’s Theory)

According to this theory, failure of the specimen subjected to any combination of the load when the maximum shearing stress at any point reaches the failure value equal to that developed at the yielding in an axial tensile or compressive test of the same material.

Maximum strain energy theory (Haigh’s theory)

According to this theory, a body complex stress fails when the total strain energy at elastic limit in simple tension.

Maximum shear strain energy / Distortion energy theory / Mises – Henky theory.

It states that inelastic action at any point in body, under any combination of stress begging, when the strain energy of distortion per unit volume absorbed at the point is equal to the strain energy of distortion absorbed per unit volume at any point in a bar stressed to the elastic limit under the state of uniaxial stress as occurs in a simple tension / compression test.

It cannot be applied to the material under hydrostatic pressure.

All theories will give same results if loading is uniaxial.

Long columns do not fail by crushing alone, but also by bending (buckling). The load at which the column just buckles, is known as buckling load or critical load or crippling load. The buckling load is less that the crushing load for long column. Buckling load for short column is higher than that of long column.

The root-mean-square speed of the molecule:

 the universal gas constant.  R has the same value for all gases: 8.3145 kJ/kmol K

The constant k is called the Boltzmann constant and is equal to the ratio of the gas constant R and the Avogadro constant N_A

According to Boyle’s law for a fixed mass of gas at constant temperature, the volume is inversely proportional to the pressure. That means that, for example, if you double the pressure, you will halve the volume. This can express this mathematically as PV = constant.
As isothermal process has constant temperature so governed by Boyle’s law.

Biot number is the ratio of internal conduction resistance within solid to external convective resistance at body surface.

Small Biot number shows conduction resistance is less important. In this case we use Lumped capacitance analysis. According to which:

Volumetric efficiency is defined as the ratio of actual volume flow rate of air into the system to the rate at which the volume is displaced by the system.

It indicates the breathing capacity of the system. It is to be noted that the utilization of the air is that determines the power output of the engine. Intake system must be designed in such a way that the engine must be able to take in as much air as possible.

A boundary layer is a thin layer of viscous fluid close to the solid surface of a wall in contact with a moving stream in which (within its thickness δ) the flow velocity varies from zero at the wall (where the flow “sticks” to the wall because of its viscosity) up to U_∞ (free stream velocity) at the boundary. In a flow field, viscous stresses are very prominent within this layer.

• A venturimeter is a device used for measuring the rate of flow of a fluid of a liquid flowing through a pipe
• The venturimeter always have smaller convergent portion and larger divergent portion
• This is done to ensures a rapid converging passage and a gradual diverging passage in the direction of flow to avoid the loss of energy due to separation
• In course of flow through the converging part, the velocity increases in the direction of flow according to the principle of continuity, while the pressure decreases according to Bernoulli’s theorem
• The velocity reaches its maximum value and pressure reaches its minimum value at the throat
• Subsequently, a decrease in the velocity and an increase in the pressure take place in course of flow through the divergent part
• The angle of convergence ≈ 20°
• The angle of divergence = 6° - 7° → It should be not greater than 7° to avoid flow separation

Density of sea water (ρ_sw) > density of river water  (ρ_rw)
For the same ship, balancing the buoyant force for both conditions,

where h is the depth of ship into the water

∴ The ship rises up when it enters the sea from a river.