Full Test 1 - EKT Mechanical - AFCAT MCQ

A = B ⇒ x² − 36 = 0 ⇒ x² = 36 ⇒ x = ±6

The given integral is of the beta function. Hence it can be written as

Here n = 4, therefore the integral becomes

A = {getting a six a atleast 1}= 1-{getting no six}

B = {getting a six on both}

Probability of getting a six on both, given atleast one die gets six i.e. Probability of B given A

Also A∩B = B


= 1/11

In the limit, we get the indeterminate form i.e. (∞⁰).
Rewriting the problem:



This implies that the n^th root of n approaches 1 as n approaches infinity.

Equilibrium is the status of the body when it is subjected to a system of forces. If the resultant force is equal to zero it implies that the net effect of the system of forces is zero this represents the state of equilibrium.

Series Circuits:
I₁ = I₂ = I
R_t = R₁ + R₂
V= V_t = V₁ + V₂

Parallel circuits:
V₁ = V₂ = V
R_t = (1/R₁) + (1/R₂)
I_t = I₁ + I₂
Power = VI = I²R = V²/R
Two bulbs when connected in parallel to a source take 100 W each.

When two bulbs are connected in series:
R_t = R₁ + R₂ = 2R

• The degree to which an object conducts electricity is known as conductance
• It is calculated as the ratio of the current which flows to the potential difference present
• This is the reciprocal of the resistance and is measured in Siemens or mhos
• Resistance is measured in ohms

The capacitance of parallel conducting wires:

Where R is the radius of the wire and d is the distance between conductors

The speed of electromagnetic waves in free space is equal to the velocity of light.

The material of the rivets must be tough and ductile. They are usually made of steel (low carbon steel or nickel steel), brass, aluminium or copper, but when strength and a fluid tight joint is the main consideration, then the steel rivets are used.

The sunk keys are provided half in the keyway of the shaft and half in the keyway of the hub or boss of the pulley.

A key attached to one member of a pair and which permits relative axial movement is known as feather key. It is a special type of parallel key which transmits a turning moment and permits axial movement.

A flat saddle key is a taper key which fits in a keyway in the hub and is flat on the shaft. It is likely to slip round the shaft under load. Therefore, it is used for comparatively light loads.

A hollow saddle key is a taper key which fits in a keyway in the hub and the bottom of the key is shaped to fit the curved surface of the shaft. Since hollow saddle keys hold on by friction, therefore these are suitable for light loads. It is usually used as a temporary fastening in fixing and setting eccentrics, cams etc.

For ball bearing:
LP³ = C
L₁P₁³ = L₂P₂³
L₂ = 8L₁

When the frictional force helps  the applied force in applying the brake, such type of brakes are said to be self energizing brakes.

When the frictional force is great enough to apply the brake with no external force, then the brake is said to be self-locking brake.
The brake should be self-energizing and not the self-locking.

If the shank of the bolt is turned down to a diameter equal to even slightly less than the core diameter of the thread, then the shank of the bolt will undergo a higher stress. This means that the shank will absorb a large portion of the energy thus relieving the material at the section near the thread. The bolt in this way becomes stronger and lighter and it increase the shock absorbing capacity of the bolt.

v² = u² + 2as

7.021 = 9.8 × sin θ
sin θ = 0.716
θ = 45.76°

Vector is a quantity that has both magnitude and direction. In contrast to vectors, ordinary quantities that have a magnitude but not a direction are called scalars. For example, displacement, velocity, and acceleration are vector quantities, while speed (the magnitude of velocity), time, and mass are scalars.

Or simply we can say that for same stress, M∝Z
If M increased to three times, then Z should increase to three times.

Polar moment of inertia of hollow shaft 

R_A = w

V_x = R_A = w
V_A = w, V_B = w
Hence, S.F.D. is as shown in figure below

In case of constant volume the entropy change is given as

For a reversible heat engine,

Gibb’s free energy function (G)
G = H – TS
G = f(H, T, S)

Heat transfer takes place according to second law of thermodynamics. Second law of thermodynamics states that “heat will flow naturally from one reservoir to another at a lower temperature, but not in opposite direction without assistance”.

Note:
The Prandtl number, Pr, is the ratio of the momentum diffusivity (kinematic viscosity) to the thermal diffusivity.

The Reynolds number (Re) is the ratio of inertia forces in the fluid to the viscous forces.

Schmidt and Sherwood numbers are the mass transfer coefficient.
Schmidt number (Sc): Ratio of molecular diffusivity of momentum to molecular diffusivity of mass transfer.

Sherwood number (Sh): Ratio of total mass transfer rate to mass transfer by molecular diffusion

Lewis Number represent the relative magnitudes of heat and mass diffusion in the thermal and concentration boundary layers.

Lorenz Number: Wiedemann–Franz law states that the ratio of the electrical to the thermal conductivity was a constant for several metals, at a given temperature.

Impulse turbine: At the inlet of the turbine, the energy available is only kinetic energy

Example: Pelton Turbine

Reaction Turbine: At the inlet of the turbine, the water possesses kinetic energy as well as pressure energy

Example: Francis Turbine, Kaplan Turbine

A hydrometer or areometer is an instrument that measures the specific gravity (relative density) of liquids-the ratio of the density of the liquid to the density of water.

A hygrometer, also known as a psychrometer, is a device that is used to measure the humidity in the air.

A thermometer is a device that measures temperature or a temperature gradient.

A piezometer is a device used to measure liquid pressure in a system by measuring the height to which a column of the liquid rises against gravity.

Cavitation is defined as the phenomenon of formation of vapour bubbles of a flowing liquid in a region where the pressure of the liquid falls below its vapour pressure and the sudden collapsing of these vapour bubbles in a region of higher pressure. When the vapour pressure collapse, very high pressure is created.

Effects of cavitation:

(i) The metallic surfaces are damaged and cavities are formed on the surfaces.

(ii) Due to the sudden collapse of the vapour bubble, considerable noise and vibrations are produced.

(iii) Due to cavitation, the metal of the runner vanes and the draft tube is gradually eaten away, which results in lowering the efficiency of the turbine.