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30 Questions MCQ Test - Full Test 5 - EKT Mechanical

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Full Test 5 - EKT Mechanical - Question 1

 

Find the value of L {a. cos at}

Detailed Solution for Full Test 5 - EKT Mechanical - Question 1

Full Test 5 - EKT Mechanical - Question 2

The angle between two vectors a = i + 2j – k and b = 2i + j + k is

Detailed Solution for Full Test 5 - EKT Mechanical - Question 2

Angle between two vectors:

θ = 60°

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Full Test 5 - EKT Mechanical - Question 3

The degree of differential equation 

Detailed Solution for Full Test 5 - EKT Mechanical - Question 3

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

Full Test 5 - EKT Mechanical - Question 4

If rank of  is 2 then λ is

Detailed Solution for Full Test 5 - EKT Mechanical - Question 4

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

Full Test 5 - EKT Mechanical - Question 5

Given P(A) = 1/4, P(B) = 1/3 and P(AUB) = 1/2. Value of P(A/B) is

Detailed Solution for Full Test 5 - EKT Mechanical - Question 5

Conditional probability P(A|B):

Full Test 5 - EKT Mechanical - Question 6

Force of buoyancy on a floating body equals ________.

Detailed Solution for Full Test 5 - EKT Mechanical - Question 6

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.

Full Test 5 - EKT Mechanical - Question 7

A Farad is defined as

Detailed Solution for Full Test 5 - EKT Mechanical - Question 7

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.

Full Test 5 - EKT Mechanical - Question 8

A car of mass 1000 kg travelling at 32 ms-1 dashes into the rear of a truck of mass 8000 kg moving in the same direction with a velocity of 4 ms-1. After the collision, the car bounces back with a velocity of 8 ms-1. What is the velocity of the truck after the impact?

Detailed Solution for Full Test 5 - EKT Mechanical - Question 8

for the car,
mcar = 1000 kg, ucar = 32 ms-1, vcar = -8 ms-1

for truck,
mtruck = 8000 kg, utruck = 4 ms-1, vtruck = ?

By conservation of linear momentum,

mcar.ucar + mtruck.utruck = mcar vcar + mtruck.vtruck
⇒ 1000 × 32 + 8000 × 4 = 1000 × (-8) + 8000 × vtruck
⇒ vtruck = 9 ms-1

Full Test 5 - EKT Mechanical - Question 9

A transformer is based on the principle of

Detailed Solution for Full Test 5 - EKT Mechanical - Question 9

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.

Full Test 5 - EKT Mechanical - Question 10

If the errors involved in the measurement of a side and mass of a cube are 3% and 4% respectively. What is the maximum permissible error in the density of the material?

Detailed Solution for Full Test 5 - EKT Mechanical - Question 10


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%.

Full Test 5 - EKT Mechanical - Question 11

Newton is unit of force. It is the unit in

Detailed Solution for Full Test 5 - EKT Mechanical - Question 11

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.

Full Test 5 - EKT Mechanical - Question 12

A key made from a cylindrical disc having segmental cross-section, is known as

Detailed Solution for Full Test 5 - EKT Mechanical - Question 12

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.

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.

Full Test 5 - EKT Mechanical - Question 13

If the tearing efficiency of a riveted joint is 60%, then ratio of rivet hole diameter to the pitch of rivets is _____.

Detailed Solution for Full Test 5 - EKT Mechanical - Question 13

Full Test 5 - EKT Mechanical - Question 14

Which of the following is a flexible coupling?

Detailed Solution for Full Test 5 - EKT Mechanical - Question 14

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
Full Test 5 - EKT Mechanical - Question 15

The difference between tensions on the tight and slack slides of a belt drive is 3000 N. If the belt speed is 15 m/sec, the transmitted power, in kW, is

Detailed Solution for Full Test 5 - EKT Mechanical - Question 15

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

Full Test 5 - EKT Mechanical - Question 16

If two equal forces of magnitude P acts at an angle θ, their resultant will be

Detailed Solution for Full Test 5 - EKT Mechanical - Question 16

Magnitude of resultant Forces F1 and F2 is:

 

Full Test 5 - EKT Mechanical - Question 17

A body of weight 30 N rests on a horizontal floor. A gradually increasing horizontal force is applied to the body which just starts moving when the force is 9 N. The coefficient of friction between the body and the floor will be

Detailed Solution for Full Test 5 - EKT Mechanical - Question 17

 

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).


Full Test 5 - EKT Mechanical - Question 18

Maximum shear stress in a beam of rectangular cross section is ________ times the average shear stress.

Detailed Solution for Full Test 5 - EKT Mechanical - Question 18

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

Full Test 5 - EKT Mechanical - Question 19

A bar of length ‘L’ cm extends by ‘I’ mm under a tensile force of ‘P’. Then, the strain produced in the bar is

Detailed Solution for Full Test 5 - EKT Mechanical - Question 19

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

Full Test 5 - EKT Mechanical - Question 20

A tensile test is performed on a round bar. After fracture, it has been found that the diameter remains approximately same at fracture. The material under test was

Detailed Solution for Full Test 5 - EKT Mechanical - Question 20

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

Full Test 5 - EKT Mechanical - Question 21

Strain rosettes are used to

Detailed Solution for Full Test 5 - EKT Mechanical - Question 21

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.

Full Test 5 - EKT Mechanical - Question 22

The maximum distortion energy theory of failure is suitable to predict the failure of which one of the following types of materials?

Detailed Solution for Full Test 5 - EKT Mechanical - Question 22

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.

Full Test 5 - EKT Mechanical - Question 23

A sample of 200 g of water is slowly heated from 27°C to 97°C. Calculate the change in entropy of the water. Specific heat capacity of water = 4200 J/kgK

Detailed Solution for Full Test 5 - EKT Mechanical - Question 23

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

Full Test 5 - EKT Mechanical - Question 24

In the Van der Waal’s gas equation the constant ‘a’ is introduced to compensate for

Detailed Solution for Full Test 5 - EKT Mechanical - Question 24


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

Full Test 5 - EKT Mechanical - Question 25

Efficiency of a Carnot engine is 75%. If the cycle direction is reverse, COP of the heat pump working on reversed Carnot cycle will be

Detailed Solution for Full Test 5 - EKT Mechanical - Question 25

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

Full Test 5 - EKT Mechanical - Question 26

Which one of the following is true for black body

Detailed Solution for Full Test 5 - EKT Mechanical - Question 26

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

Full Test 5 - EKT Mechanical - Question 27

The product of diameteral pitch and circular pitch is

Detailed Solution for Full Test 5 - EKT Mechanical - Question 27

Full Test 5 - EKT Mechanical - Question 28

The barometric pressure at the base of a mountain is 750 mm Hg and at the top 600 mm Hg. if the average air density is 1 kg/m3, the height of the mountain (in m) is approximately

Detailed Solution for Full Test 5 - EKT Mechanical - Question 28

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

⇒ Height of mountain = 2040 m

Full Test 5 - EKT Mechanical - Question 29

The expression  commonly used to express Bernoulli’s equation, has units of total energy per unit

Detailed Solution for Full Test 5 - EKT Mechanical - Question 29

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

Full Test 5 - EKT Mechanical - Question 30

The unit of the following property is not m2/s

Detailed Solution for Full Test 5 - EKT Mechanical - Question 30

Thermal diffusivity, 

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

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