Full Test 4 - EKT Mechanical - AFCAT MCQ

Total balls in the bag are = 15
Sample space 
The probability that all the balls are red is 

Multiplying matrix A by itself, we get 

We know that 1 + ω  +ω²  = 0 and ω³ = 1 then

(1−ω⁸)(1−ω⁴)(1−ω²)(1−ω) = (1−ω²)(1−ω)(1−ω²)(1−ω)
= (1−ω²−ω+ω³)(1−ω²−ω+ω³)
= (2−(ω+ω²))(2−(ω+ω²))
= (2−(−1))(2−(−1)) = 9

The determinant if matrix A is given as

Viscosity is the property of a fluid which determines its resistance to shearing stresses or which opposes the relative motion between the different layers.

Cause of Viscosity: It is due to cohesion and molecular momentum exchange between fluid layers.

S.I. Units: Pa.s or N.s/m²
C.G.S Unit of viscosity is Poise = dyne-sec/cm²
One Poise = 0.1 Pa.s
1/100 Poise is called centipoises.
Dynamic viscosity of water at 20^oC is approx = 1 cP

Tesla (T) is a measure of magnetic flux density.
Electrical potential measures in volts (V).
Magnetic potential measures in Amperes (A).

Optical fibre works on the principle of total internal reflection. Here light is used to transmit information from one place to another.

Color in soap bubble is due to phenomenon of thin film interference. There is a thin film like structure formed between the outer and inner surface of the bubble, which reflects a spectrum of beautiful colors from its surface.

A zener diode works based on the tunneling of charge carriers across the junction. A zener diode is a normal diode in the forward biased. It is in the reverse biased condition that the heavy doping causes a zener to behave differently than a normal diode.

The notation of rope is given as

A line AB is parallel to both HP and VP. Its side view will be a point.

Or it can be viewed as:

Square and trapezoidal threads are most commonly used threads.

Square thread: In this thread the flanks are perpendicular to the axis of the thread. This is used for transmitting motion or power. E.g. Fly presses, Screw jack, vice handles, cross-slide and compound slide etc.

Trapezoidal threads: These threads have a profile which is neither square nor V thread form and have a form of trapezoid. Different forms of trapezoidal threads are ACME thread, Buttress thread, Saw-tooth thread, Worm thread

• ACME thread: It has an included angle of 29°. These are used in lathe lead screws.
• Buttress Thread: In this thread, one flank is perpendicular to the axis of the thread and other flank is at 45°. These threads are used in power press, carpentry vices, gun breeches, ratchets etc.
• Knuckle thread: The shape of the knuckle thread is not trapezoid, but it has a rounded shape. It has limited applications. It is used for valve spindles, railway carriage coupling, hose connections etc.

Power transmitted 

Where T₁ and T₂ = Tensions in the tight and slack side of the belt respectively in newton
v = Velocity of the belt in m/s

Barth Key: It is modification of rectangular key which has two bevelled surfaces. The bevelled surface ensure that key will fit tightly. Primarily key is under compression rather than in shear.

Acceleration (a) = dv/dt = 3t² − 2t
at t = 3 sec
a = 3 × 3 × 3 – 2 × 3 = 21 m/s²

According to Newton’s Second Law of Motion, the applied force or impressed force is directly proportional to the rate of change of momentum.

Newton’s second law of motion gives the measure of force as F = ma.

According to Second law of motion the net force acting on a body is equal to the product of the mass of body and the acceleration produced in it OR the acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object

Core of a cross section of a column is defined as the portion of cross section of a column within which the eccentric axial load should act so that there is no tensile stress developed on the cross section of the column. The diameter of core of a circular section is d/4.

For thick cylinder:

(Radial stress always compressive so its magnitude always negative)

These two equations are called Lame’s Equations. The constants A and B are obtained from the boundary conditions.

The ratio of lateral strain to the longitudinal strain is a constant for a given material, when the material is stressed within the elastic limit. This ratio is known as Poisson’s ratio (μ).

Shear force is the rate of change of bending moment. Let F is shear force, M is bending moment and W is load then

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

A diathermal or diabatic wall is one that heat can pass through. It is made from a thermal conductor. It is essentially a thermal wall.

An adiabatic wall is one that heat cannot pass through. It is made from a thermal insulator.

P = intensive property
dV = change in extensive property

The enthalpy of a substance H is defined as

H = U + PV

Hence, the enthalpy is calculated as the sum of internal energy and the product of pressure and volume of the system

It is an extensive property of a system and its unit is kJ.

So it is form of energy with the dimensional unit  ML²T^-2

Carnot cycle consists of two reversible isothermal and two isentropic process.

Bernoulli's equation states that the summation of pressure head, kinetic head and datum/potential head is constant for steady, incompressible, irrotational and non-viscous flow. In other words an increase in the speed of the fluid occurs simultaneously with a decrease in pressure or a decrease in the fluid's potential energy i.e. the total energy of a flowing system remain constant until external force is applied. So Bernoulli’s equation refers to conservation of energy.

All flow measuring devices like Venturimeter, Orifice meter, Pitot tube meter works on the Bernoulli’s theorem.

A piezometer is either a device used to measure liquid pressure in a system by measuring the height to which a column of the liquid rises against gravity, or a device which measures the pressure (more precisely, the piezometric head) of groundwater at a specific point.