Full Test 2 - EKT Mechanical - AFCAT MCQ

Order of the differential equation is the highest derivative in a differential equation. Hence the order is 2. 

The system of homogeneous linear equations has a non – trivial solution if

(4a – 1)² = 0
a = 1/4 

If u is a homogeneous function of degree n in x and y, then according to Euler’s Theorem:

The slope of the line joining the origin to the center is m₁ (-8/6)
A tangent is perpendicular to the radius at the point of contact, so it’s slope will be m₂ (-1/m₁ ) = (6/8)
Equation of line will be: y = mx

As, the line passes through the origin, so there’s no constant term c (recall y = mx + c)

A stream lined body is defined as the body whose surface coincides with the stream - lines, when the body is placed in a flow. In that case the separation of flow will take place only at trailing edge (or rearmost part of the body).

Behind a stream lined body, wake formation zone will be very small and consequently the pressure drag will be very small. Thus the total drag on the stream lined body will be due to friction (shear) only.

By conservation of angular momentum
I’ω’ = Iω
(M + 2m) r²ω’ = Mr²ω

The current at a point in the circuit is the amount of charge that passes that point in one second. A current of 1 A is flowing in a circuit if a charge of 1 coulomb passes any point in the circuit every second.

In an AC circuit, resonance occurs when capacitive reactance equals reactive reactance.
At resonance, X_L = X_C,Z = R

• For every material, there is a temperature specific to it known as its Curie temperature
• Above curie temperature, they lose their magnetic properties

In AutoCAD, to specify the drawing units in a new or existing drawing, the drafter should set the units to decimal. Decimal unit set is the default unit system in AutoCAD.

A brake is a device by means of which artificial frictional resistance is applied to a moving machine member,in order to retard or stop the motion of a machine.

In the process of performing this function, the brake absorbs either kinetic energy of the moving member or potential energy given up by objects being lowered by hoists, elevators etc.The energy absorbed by brakes is dissipated in the form of heat. This heat is dissipated in the surrounding air.

Key is the weakest member in the assembly of shaft, pulley and key. Key acts as a safety device, whenever there is excess load appears on the pulley key fails first and it keeps safer to shaft and pulley.

A bearing is said to be hydrostatic bearing if it has a static fluid (liquid or air) along the surface of the shaft/journal where the fluid will be supplied externally and the pressure is generally maintained by an external pump; thus enabling non-contacting operation and the ability to support a load. Hydrostatic bearings can support large loads without journal rotation and provide large (accurate and controllable) direct stiffness as well as damping (energy dissipation) coefficients.

In case of hydrodynamic bearing the pressure is developed by the high speed journal at higher rpm, this helps the movement of thin film of lubricant. For Journal bearings mostly converging fluids are employed.

Number of pair of contact surfaces = n = n₁ + n₂ – 1
Where, n₁ is the number of discs on driving shaft
N₂  is the number of discs on driven shaft
N = 6 + 5 – 1 = 10

∴ the speed of the smaller object is higher than that of bigger.

Momentum of the smaller object:
 

Lighter body will have smaller momentum.

Force = T - W
ma = T - W
Acceleration is given as

Tension is given as
T = mg + ma = m (g + a)
T = 1000 (10 + 2)
T = 12000 N

Whenever the bar is subjected to the axial tensile load, there will be increase in the length of the bar along the direction of the loading.

Longitudinal strain is defined as the ratio of increase in length of the bar in the direction of applied load to that of the original length.

A cantilever beam subjected to point load on free end will have maximum bending moment at fixed end and constant shear force throughout the length. So maximum stress will be at fixed end (σ = My/I) and failure will occur at that point.

From SFD and BMD Diagram, we can conclude that shear force and Bending moment both are zero when cantilever beam is subjected to uniformly distributed load.

Salient points of Stress-Strain Diagram:

Point A (Limit of proportionality or the proportionality limit): The strain is proportional to strain or elongation is proportional to the load giving a st.line relationship. This law of proportionality is valid upto a point A.

Point B (Elastic Limit): For a short period beyond the point A, the material may still be elastic in the sense that the deformations are completely recovered when the load is removed.

Point (C) and (D) - Beyond the elastic limit plastic deformation occurs and strains are not totally recoverable. There will be thus permanent deformation or permanent set when load is removed. These two points are termed as upper and lower yield points respectively.

Yield stress is defined as the stress after which material extension takes place more quickly with no or little increase in load.

Point E: A further increase in the load will cause marked deformation in the whole volume of the metal. The maximum load which the specimen can with stand without failure is called the load at the ultimate strength.

Point F: Beyond point E, the bar begins to forms neck. The load falling from the maximum until fracture occurs at F.

Compressibility (τ):

Compressibility is thus inverse of bulk modulus. Hence compressibility can be defined as the incurred volummetric strain for unit change in pressure.
Isentropic compressibility: 
Isothermal compressibility:  
Since: PV=nRT

Hence, isothermal compressibility is

Q  = mcΔT = 5 × 4.2 × (100−20) = 1680kJ

The variation in thermal conductivity of a material with temperature in the temperature range of interest is given by k(T) = k₀ (1 + αT) where α is called the temperature coefficient of thermal conductivity.

Curve B represents that α is less than zero
Curve D represents that α is zero
Curve A represents that α is greater than zero

Curve C represents that α is very large so the value of thermal conductivity is also very large. Curve C represents that there is almost no loss in heat transfer across the thickness which clearly indicates very large value of thermal conductivity.

Absolute entropy (S) or entropy is a measure of energy dispersion in a system.

Following are basic features of entropy:

• Entropy transfer is associated with heat transfer (direction of flow of entropy is same as that of heat flow)
• Entropy is proportional to mass flow in an open system
• Entropy does not transfer with work

Entropy linked with energy

Discharge through a pipe is Q = AV

Absolute pressure = Gauge pressure + atmospheric pressure  = 25 + 1.03 = 26.03 bar

High head turbine: In this type of turbines, the net head varies from 150m to 2000m or even more, and these turbines require a small quantity of water. Example: Pelton wheel turbine.

Medium head turbine: The net head varies from 30m to 150m, and also these turbines require a moderate quantity of water. Example: Francis turbine.

Low head turbine: The net head is less than 30m and also these turbines require a large quantity of water. Example: Kaplan turbine.