Full Test 5 - EKT Mechanical - AFCAT MCQ

Angle between two vectors:

θ = 60°

The degree of the differential equation is the highest order of differentiation provided there are no radial in the equation.
So, we take the term to the right side and square both sides to remove the radical.

Hence, in the given problem the degree is 2.
Also the order of differential equation is 2

The given matrix is

The determinant is given as |A| = λ³ – 1
If ⍴(A) is given as 2, then the determinant of A should be zero
⇒ |A| = 0 ⇒ λ³ – 1 = 0;
We get λ = 1  at which there are more than one 22 sub-matrices having non zero determinant
∴ value of λ is 1 for which rank of A is 2

Conditional probability P(A|B):

When a body is immersed in a fluid, an upward force is exerted by the fluid on the body.
This upward force is equal to the weight of the fluid displaced by the body and is called the force of buoyancy.

1 farad = 1 coulomb/volt
One farad is defined as the capacitance of a capacitor which requires a charge of one coulomb to establish a potential difference of one volt between its plates.

for the car,
m_car = 1000 kg, u_car = 32 ms^-1, v_car = -8 ms^-1

for truck,
m_truck = 8000 kg, u_truck = 4 ms^-1, v_truck = ?

By conservation of linear momentum,

m_car.u_car + m_truck.u_truck = m_car v_car + m_truck.v_truck
⇒ 1000 × 32 + 8000 × 4 = 1000 × (-8) + 8000 × v_truck
⇒ v_truck = 9 ms^-1

A transformer is a static device which converts electrical power from one circuit to another without changing its frequency. It Steps up (or Steps down) the level of AC Voltage and Current. The transformer works on the principle of mutual induction of two coils or Faraday Law’s of electromagnetic induction. When the current in the primary coil is changed the flux linked to the secondary coil also changes. Consequently, an EMF is induced in the secondary coil due to Faraday laws of electromagnetic induction.

The percentage error in density is given by,

= 4% - 3 × 3% = - 5%
Hence, the maximum permissible error in the density of the material is 5%.

The MKS unit of force, the newton, is the force which accelerates a mass of one kilogram at the rate of one meter per second per second. The corresponding unit in the CGS system is the dyne; there are 105 dynes in one newton.

The woodruff key is an easily adjustable key. It is a piece from a cylindrical disc having segmental cross-section. This key is largely used in machine tool and automobile construction.

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 also 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. 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.

Gib-head key is a rectangular sunk key with a head at one end known as gib head. It is usually provided to facilitate the removal of key.

Couplings are devices used to connect two shafts together and are divided into two categories: Rigid and Flexible. Both are used for the purpose of transmitting power, rigid couplings being more limited in applications as compared to flexible couplings. Rigid couplings are used where shafts are already positioned in precise lateral and angular alignment. Their design does not allow for any misalignment between shafts, but are generally able to transmit more power than flexible couplings. Flexible couplings are designed to accommodate misalignment between shafts and various types of load conditions.

Types of Rigid Couplings

• Sleeve or muff coupling
• Clamp coupling, compression coupling or split muff coupling
• Flange coupling
• Marine coupling

Types of Flexible Couplings

• Universal Joints
• Oldham Couplings
• Flexible Shaft Couplings

T₁ − T₂ = 3000N 
Speed of belt, V = 15 m/sec
P = (T₁ – T₂) V
= 3000 × 15 = 45 KW

Magnitude of resultant Forces F₁ and F₂ is:

 

The ratio of the limiting force of friction (F) to the normal reaction (R or N) between two bodies is known as co-efficient of friction (μ).

Maximum shear stress of rectangular section, maximum stress occur at neutral axis________

Strain is the ratio of change in length to the original length.

Ductile material fails along principal shear plane as they are weak in shear and brittle material fails along principal normal stress.

The strain rosette is a device used to measure normal strain at a point in a plane. It comprises three independent strain gauges, each of which is used to read strain at the same point but in a different direction.

According to maximum distortion energy theory  or Von Mises theory a given structural material is safe as long as the maximum value of distortion energy per unit volume in that material remains smaller than the distortion energy per unit volume required to cause yield in a tensile- test specified of the same material. Maximum distortion energy theory of failure is suitable to predict the failure of ductile materials.

The heat supplied to increase the temperature of the sample is
ΔQ = mCΔT
Where m = 0.2 kg
C = 4200 J/kg-K

Total change in entropy as the temperature rises from T₁ to T₂ is

a → accounts for intermolecular forces.
b → accounts for volume occupied by gas molecules.

Efficiency of Carnot cycle 
By reversing the Carnot cycle we can have either heat pump or refrigerator.
COP of heat pump 

Since black body is perfect absorber of radiation hence absorptivity of black body α = 1.

α + τ + ρ = 1 so for black body τ = ρ = 0.
White body: ρ = 1 so τ = α = 0
Transparent body: τ = 1 so α = ρ = 0
Opaque body: τ = 0

At base P_B = 750 mm of Hg
At top, P_A = 600 mm of Hg
∴ Pressure difference = 150 mm of Hg
(ΔP) = hρg

⇒ Height of mountain = 2040 m

The expression  has units of total energy per unit volume.
If expression is like  , then it is energy per unit weight.

Thermal diffusivity, 

Kinematic viscosity, 
Dynamic viscosity, μ has unit Pa.S
Mass diffusivity has also unit of (m²/S)