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# Past Year Paper - Mechanical Engineering GATE : 2019

## 65 Questions MCQ Test GATE Mechanical (ME) 2022 Mock Test Series | Past Year Paper - Mechanical Engineering GATE : 2019

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This mock test of Past Year Paper - Mechanical Engineering GATE : 2019 for GATE helps you for every GATE entrance exam. This contains 65 Multiple Choice Questions for GATE Past Year Paper - Mechanical Engineering GATE : 2019 (mcq) to study with solutions a complete question bank. The solved questions answers in this Past Year Paper - Mechanical Engineering GATE : 2019 quiz give you a good mix of easy questions and tough questions. GATE students definitely take this Past Year Paper - Mechanical Engineering GATE : 2019 exercise for a better result in the exam. You can find other Past Year Paper - Mechanical Engineering GATE : 2019 extra questions, long questions & short questions for GATE on EduRev as well by searching above.
QUESTION: 1

### A final examination is the __________ of a series of evaluations that a student has to go through.

Solution:

A final examination is the culmination of a series of evaluations that a student has to go through. Meaning of culmination is the highest or climactic point of something, especially as attained after a long time Hence, it is the most appropriate word

QUESTION: 2

### If IMHO = JNIP; IDK = JEL; and SO = TP, then IDC = __________.

Solution:

I+1=J, M + 1 = N, H + 1 = I, O + 1 = P; I + 1 = J, D + 1 = E, K + 1 = L; S + 1 = T, O + 1 = P
Hence, IDC will be written as JED
I + 1 = J, D + 1 = E, C + 1 = D

QUESTION: 3

### Are there enough seats here? There are __________ people here than I expected.

Solution:

Comparison is made here between the number of people and number of seats, hence, more is the most appropriate word

QUESTION: 4

Once the team of analysts identify the problem, we ________ in a better position to comment on the issue.Which one of the following choices CANNOT fill the given blank?

Solution:

Since the 1st clause is in present tense, the second clause will not use past tense.are going to be, will be, might be fill the given blank appropriately.

QUESTION: 5

The product of three integers X, Y and Z is 192. Z is equal to 4 and P is equal to the average of X and Y. What is the minimum possible value of P?

Solution:

XYZ = 192 and Z = 4
So, XY = 48

For finding the minimum possible of P, X + Y should be minimum
Now, the possible values of X and Y are as follows

So, from this we can clearly see that X + Y will be minimum only when X = 8 and Y = 6 or vice-versa
So minimum value of P

QUESTION: 6

X is an online media provider. By offering unlimited and exclusive online content at attractive prices for a loyalty membership, X is almost forcing its customers towards its loyalty membership. If its loyalty membership continues to grow at its current rate, within the next eight years more households will be watching X than cable television.Which one of the following statements can be inferred from the above paragraph?

Solution:

option A is the most appropriate solution

QUESTION: 7

Fiscal deficit was 4% of the GDP in 2015 and that increased to 5% in 2016. If the GDP increased by 10% from 2015 to 2016, the percentage increase in the actual fiscal deficit is ____________.

Solution:

Let the GDP in 2015 = x
Then, the GDP in 2016 will be = 1.1x
So, fiscal deficit in 2015 = 0.04×x=0.04x
And the fiscal deficit in 2016 = 0.05×1.1x=0.055x
Increase in fiscal deficit = 0.055x – 0.04x = 0.015x
So, the percentage increase in fiscal deficit = ×100=37.5%

QUESTION: 8

Two pipes P and Q can fill a tank in 6 hours and 9 hours respectively, while a third pipe R can empty the tank in 12 hours. Initially, P and R are open for 4 hours. Then P is closed and Q is opened. After 6 more hours R is closed. The total time taken to fill the tank (in hours) is _________.​

Solution:

1 hour work of P = 1/6
1 hour work of Q = 1/9
1 hour work of R = -1/12 (negative sign indicates that its emptying the tank)
Tank filled when P and R works initially for 4 hours =
Tank filled by when Q and R works for another 6 hours =
Total tank filled in these 10 hours =
So, the remaining half tank will be filled by Q alone in 4.5 hours (Since Q can fill the complete tank in 9 hours)
Therefore, total time required to fill the tank =4 + 6 + 4.5 = 14.5 hours

QUESTION: 9

While teaching a creative writing class in India, I was surprised at receiving stories from the students that were all set in distant places: in the American West with cowboys and in Manhattam penthouses with clinking ice cubes. This was, till an eminent cAribbean writer gave the writers in the once-colonised countries the confidence to see the shabby lives around them as worthy of being “told”.The writer of this passage is surprised by the creative writing assignments of his students, because __________.

Solution:
QUESTION: 10

Mola is a digital platform for taxis in a city. It offers three types of rides – Pool, Mini and Prime. The Table below presents the number of rides for the past four months. The platform earns one US dollar per ride. What is the percentage share of revenue contributed by Prime to the total revenues of Mola, for the entire duration?

Solution:

Revenue contributed by Pool = 170 + 320 + 215 + 190 = 895
Revenue contributed by Mini = 110 + 220 + 180 + 70 = 580
Revenue contributed by Prime = 75 + 180 + 120 +90 = 465
Total revenue of Mola = 895 + 580 + 465 = 1940
So, the percentage share =

*Answer can only contain numeric values
QUESTION: 11

A wire of circular cross-section of diameter 1.0 mm is bent into a circular arc of radius 1.0 m by application of pure bending moments at its ends. The Young’s modulus of the material of the wire is 100 GPa. The maximum tensile stress developed in the wire is ____________ MPa.

Solution:

Tensile stress

*Answer can only contain numeric values
QUESTION: 12

In an electrical discharge machining process, the breakdown voltage across inter electrode gap (IEG) is 200 V and the capacitance of the RC circuit is 50 μF. The energy (in J) released per spark across the IEG is __________

Solution:

*Answer can only contain numeric values
QUESTION: 13

If x is the mean of data 3, x, 2 and 4, then the mode is _________

Solution:

QUESTION: 14

The cold forming process in which a hardened tool is pressed against a workpiece (when there is relative motion between the tool and the workpiece) to produce a roughened surface with a regular pattern is

Solution:

We provide special pattern to prevent the relative motion between contact surface. This special pattern is known as Knurling.

QUESTION: 15

Endurance limit of a beam subjected to pure bending decreases with

Solution:

Form above formula it is clear that the Endurance limit increases with increase in size, surface, load, temp and endurance strength.

QUESTION: 16

In matrix equation [A] {X} = {R}.

One of the eigenvalues of matrix [A] is

Solution:

[A] {X} = {R}.
We know AX = λX ; Where λ − Eigen Value

Hence, λ = 16

*Answer can only contain numeric values
QUESTION: 17

Water enters a circular pipe of length L = 5.0 m and diameter D = 0.20 m with Reynolds number
ReD = 500. The velocity profile at the inlet of the pipe is uniform while it is parabolic at the exit.
The Reynolds number at the exit of the pipe is___________.

Solution:

From above expiration, Reynold’s Number is independent of flow profile. Hence, Reynold’s Number for parabolic flow profile is 500.

QUESTION: 18

For a simple compressible system, v, s, p and T are specific volume, specific entropy, pressure
and temperature, respectively. As per Maxwell’s relations,  is equal to

Solution:

From mathematical relation expiration

QUESTION: 19

Hardenability of steel is a measure of

Solution:

The depth to which required hardening is obtained when it is austenitized and then quenched.

QUESTION: 20

The directional derivative of the function f(x, y) = x2 + y2 along a line directed from (0, 0) to (1,
1), evaluated at the point x = 1, y = 1 is

Solution:

Directional derivative of function along the line is the scalar value of derivative along the line. i.e.
we have to calculate value of derivative of function in the direction of given line vector

QUESTION: 21

A spur gear has pitch circle diameter D and number of teeth T. The circular pitch of the gear is

Solution:

circular pitch =

QUESTION: 22

A rigid triangular body, PQR, with sides of equal length of 1 unit moves on a flat plane. At the
instant shown, edge QR is parallel to the x-axis, and the body moves such that velocities of
points P and R are VP and VR, in the x and y directions, respectively. The magnitude of the
angular velocity of the body is

Solution:

The given body is a rigid body; Hence the given body will not have any deformation, and the possible motion is translation and angular motion. we know that the angular motion of the object is
always defined as the motion about the point. Hence, first we have to find a point parallel to both
velocity VP and VR.

∴ Angular velocity,

QUESTION: 23

Sphere 1 with a diameter of 0.1 m is completely enclosed by another sphere 2 of diameter 0.4
m. The view factor F12 is

Solution:

F12 = 1

QUESTION: 24

The transformation matrix for mirroring a point in x – y plane about the line y = x is given by

Solution:

The transformation matrix for mirroring a point in x – y plane about the line y = x is given by

*Answer can only contain numeric values
QUESTION: 25

The state of stress at a point in a component is represented by a Mohr’s circle of radius 100 MPa centered at 200 MPa on the normal stress axis. On a plane passing through the same point, the normal stress is 260 MPa. The magnitude of the shear stress on the same plane at the same point is ___________ MPa.

Solution:

QUESTION: 26

One-dimensional steady state heat conduction takes place through a solid whose cross-sectional area varies linearly in the direction of heat transfer. Assume there is no heat generation in the solid and the thermal conductivity of the material is constant and independent of temperature. The temperature distribution in the solid is

Solution:

Let the given body cross-sectional area varies linearly, and heat is flowing from left to right.

QUESTION: 27

An analytic function f(z) of complex variable z = x + l y may be written as f(z) = u(x, y) + iv (x,
y). Then, u(x, y) and v(x, y) must satisfy

Solution:

If f(z) = u(x, y) + iv(x, y) is analytic function then it must satisfy the following relations.

*Answer can only contain numeric values
QUESTION: 28

A thin vertical flat plate of height L, and infinite width perpendicular to the plane of the figure, is
losing heat to the surroundings by natural convection. The temperatures of the plate and the
surroundings, and the properties of the surrounding fluid, are constant. The relationship between
the average Nusselt and Rayleigh numbers is given as Nu = K Ra ¼, where K is a constant. The
length scales for Nusselt and Rayleigh numbers are the height of the plate. The height of the
plate is increased to 16L keeping all other factors constant.

If the average heat transfer coefficient for the first plate is h1 and that for the second plate is h2,
the value of the ratio h1/h2 is____________.

Solution:

QUESTION: 29

Which one of the following modifications of the simple ideal Rankine cycle increases the thermal efficiency and reduces the moisture content of the steam at the turbine outlet?

Solution:

Due to increase of the turbine inlet temperature, quality of the stream at outlet of the turbine improves. Which increases the thermal efficiency and reduces the moisture content of the steam at the turbine outlet.

QUESTION: 30

Consider a linear rectangular thin sheet of metal, subjected to uniform uniaxial tensile stress of 100 MPa along the length direction. Assume plane stress conditions in the plane normal to the thickness. The Young’s modulus E = 200 MPa and Poisson’s ratio v = 0.3 are given. The principal strains in the plane of the sheet are

Solution:

*Answer can only contain numeric values
QUESTION: 31

The figure shows an idealized plane truss. If a horizontal force of 300 N is applied at point A, then the magnitude of the force produced in member CD is ________N.

Solution:

The momentum about the point A must be zero, because there is no deformation of any truss.
Hence,FCD  = 0 [FCD is not passing through the point A]

QUESTION: 32

The fluidity of molten metal of cast alloys (without any addition of fluxes) increases with increase in​

Solution:

Fluidity of molten metal of cast alloys increases with increase in degree of superheat.

QUESTION: 33

The most common limit gage used for inspecting the hole diameter is

Solution:

The most common limit gage used for inspecting the hole diameter is Plug gage.

QUESTION: 34

The differential equation is valid in the domain 0 ≤ x ≤ 1 with y(0) = 2.25. The
solution of the differential equation is

Solution:

The given equation is.

Now for at x=0,

QUESTION: 35

A two-dimensional incompressible frictionless flow field is given by u = xÎ − yj. If ρ is the density
of the fluid, the expression for pressure gradient vector at any point in the flow field is given as

Solution:

Euler’s Equation of motion in 2D.

As there is no extra force acting on the fluid.

*Answer can only contain numeric values
QUESTION: 36

A short shoe external drum brake is shown in the figure. The diameter of the brake drum is 500 mm. The dimensions a = 1000 mm, b = 500 mm and c = 200 mm. The coefficient of friction between the drum and the shoe is 0.35. The force applied on the lever F = 100 N as shown in the figure. The drum is rotating anti-clockwise. The braking torque on the drum is _______N.m (round off to two decimal places).

Solution:

*Answer can only contain numeric values
QUESTION: 37

A uniform disc with radius r and a mass of m kg is mounted centrally on a horizontal axle of negligible mass and length of 1.5r. The disc spins counter-clockwise about the axle with angular speed ω, when viewed from the right-hand side bearing, Q. The axle precesses about a vertical axis at ωp = ω/10 in the clockwise direction when viewed from above. Let RP and RQ (positive upwards) be the resultant reaction forces due to the mass and the gyroscopic effect, at bearings P and Q, respectively. Assuming ω2r = 300 m/s2 and g = 10 m/s2, the ratio of the larger to the smaller bearing reaction force (considering appropriate signs) is __________.

Solution:

Reaction at P and Q due to GC

*Answer can only contain numeric values
QUESTION: 38

The figure shows a pouring arrangement for casting of a metal block. Frictional losses are negligible. The acceleration due to gravity is 9.81 m/s2. The time (in s, round off to two decimal places) to fill up the mold cavity (of size 40 cm × 30 cm × 15 cm) is ____________

Solution:

QUESTION: 39

The activities of a project, their duration and the precedence relationships are given in the table. For example, in a precedence relationship “X < Y, Z” means that X is predecessor of activities Y and Z. The time to complete the activities along the critical path is ____________ weeks.

Solution:

QUESTION: 40

The crank of a slider-crank mechanism rotates counter-clockwise (CCW) with a constant angular velocity ω, as shown. Assume the length of the crank to be r.

Using exact analysis, the acceleration of the slider in the y-direction, at the instant shown, where the crank is parallel to x-axis, is given by

Solution:

Velocity of point A, VA= r ×ω
The radial acceleration of point A, aoa=rω2
Since, the inclination of line AB is 45 degree, the acceleration of the point B will be equal to the acceleration of point A. i.e. rω​2

*Answer can only contain numeric values
QUESTION: 41

A gas tungsten arc welding operation is performed using a current of 250 A and an arc voltage of 20 V at a welding speed of 5 mm/s. Assuming that the arc efficiency is 70%, the net heat input per unit length of the weld will be ________ kJ/mm (round off to one decimal place).

Solution:

*Answer can only contain numeric values
QUESTION: 42

Water flows through two different pipes A and B of the same circular cross-section but at different flow rates. The length of pipe A is 1.0 m and that of pipe B is 2.0 m. The flow in both the pipes is laminar and fully developed. If the frictional head loss across the length of the pipes is same, the ratio of volume flow rates QB/QA is ______ (round off to two decimal places).

Solution:

QUESTION: 43

Consider two concentric circular cylinders of different materials M and N in contact with each
other at r = b, as shown below. The interface at r = b is frictionless. The composite cylinder
system is subjected to internal pressure P. Let anddenote the radial and
tangential displacement and stress components, respectively, in material M Similarly,and  denote the radial and tangential displacement and stress components, respectively,
in material N. The boundary conditions that need to be satisfied at the frictionless interface
between the two cylinders are :

Solution:

Internal pressure causes the stress in radial as well as circumferential direction.
At r=b i.e. interference of the cylinder can be frictionless if Stress in radial direction must be equal. Velocity in radial direction must be equal. (This condition will make the normal force Zero)
As radius of the cylinder increases due to inside pressure, there will be relative velocity between the contact surfaces in the circumferential direction.

QUESTION: 44

The binary phase diagram of metals P and Q is shown in the figure. An alloy X containing 60% P and 40% Q (by weight) is cooled from liquid to solid state. The fractions of solid and liquid (in weight percent) at 1250°C, respectively, will be

Solution:

*Answer can only contain numeric values
QUESTION: 45

The annual demand of valves per year in a company is 10,000 units. The current order quantity is 400 valves per order. The holding cost is Rs. 24 per valve per year and the ordering cost is Rs. 400 per order. If the current order quantity is changed to Economic Order Quantity, then the saving in the total cost of inventory per year will be Rs. __________ (round off to two decimal places).

Solution:

Annual Demand (D) = 10000 nos
Order Quantities (Q) = 400 / order
Holding cost (Ch)= 24 /valve/year
Ordering Cost (CO) = RS 400 /order

QUESTION: 46

A slender uniform rigid bar of mass m is hinged at O and supported by two springs, with stiffnesses 3k and k, and a damper with damping coefficient c, as shown in the figure. For the system to be critically damped, the ratio c/√km should be

Solution:

When System is critically Damped
Suppose that we apply a external force downward at horizontal road at spring constant 3K and leave it freely for to and fro motion.

Now, moment of inertia of rod about the center of the rod is
And moment of inertia about the hinged point is I0=
As we know that for critical dumping, the root of the quadratic equation should be real and equal.

*Answer can only contain numeric values
QUESTION: 47

The probability that a part manufactured by a company will be defective is 0.05. If 15 such parts
are selected randomly and inspected, then the probability that at least two parts will be
defective is __________ (round off to two decimal places).

Solution:

Total no. of parts = 15
P[defective(p)] = 0.05
P[non-defective(q)] = 1 – 0.05 = 0.95
P[at least 2 defective] = 1 – [P(no defective)+P(1 defective)]
Using the binomial distribution,
P[at least 2 defective] = 1 – [15C0p0q15 + 15C1p1q14]= 1 – [0.0500.9515 + 15× 0.05 × 0.9514] = 1 – [0.4639 + 0.3657] = 1 – 0.8296 = 0.1704

*Answer can only contain numeric values
QUESTION: 48

A four bar mechanism is shown in the figure. The link numbers are mentioned near the links.
Input link 2 is rotating anti-clockwise with a constant angular speed ω2. Length of different links
are :

The magnitude of the angular speed of the output link 4 is ω4 at the instant when link 2 makes
an angle of 90o with O2O4 as shown. The ratio  is __________ (round off to two decimal
places).

Solution:

Using Instantaneous center method

*Answer can only contain numeric values
QUESTION: 49

Two masses A and B having mass ma and mb, respectively, lying in the plane of the figure shown, are rigidly attached to a shaft which revolves about an axis through O perpendicular to the figure. The radii of rotation of the masses ma and mb are ra and rb, respectively. The angle between lines OA and OB is 90°. If ma = 10 kg, mb = 20 kg, ra = 200 mm and rb = 400 mm, then the balance mass to be placed at a radius of 200 mm is _________ kg (round off to two decimal places).

Solution:

Let the balance mass be m

Now, since the radius of the balance mass is 200mm, therefore m=

QUESTION: 50

A prismatic, straight elastic, cantilever beam is subjected to a linearly distributed transverse load as shown below. If the beam length is L, Young’s modulus E, and area moment of inertia I, the magnitude of the maximum deflection is

Solution:

The maximum deflection of the cantilever beam subjected to uniformly varying load (UVL) is given by

QUESTION: 51

Given a vector and nˆ as the unit normal vector to the surface of the
hemisphere (x2 + y2 + z2 = 1;z ≥0), the value of integral  evaluated on the
curved surface of the hemisphere S is

Solution:

Hemisphere (x2 + y2 + z2 = 1;z ≥0)

To find the integration of the given expiration, it is easy if we are using the stoke’s theorem.
Surface integral will become line integral.

Now, putting the value of u in the above equation.

Now converting the above equation into polar coordinate
x2+y2=r2

*Answer can only contain numeric values
QUESTION: 52

The thickness of a sheet is reduced by rolling (without any change in width) using 600 mm diameter rolls. Neglect elastic deflection of the rolls and assume that the coefficient of friction at the roll-workpiece interface is 0.05. The sheet enters the rotating rolls unaided. If the initial sheet thickness is 2 mm, the minimum possible final thickness that can be produced by this process in a single pass is ________ mm (round off to two decimal places).

Solution:

QUESTION: 53

A ball of mass 3 kg moving with a velocity of 4 m/s undergoes a perfectly-elastic direct-central impact with a stationary ball of mass m. After the impact is over, the kinetic energy of the 3 kg ball is 6 J. The possible value (s) of m is/are

Solution:

Conservation of momentum gives m1u1 + m2u2 = m1v1 + m2v2
m1=3kg, u1=4m/s, m2=m kg, u2=0
Substituting in the above equation,
3×4+m×0=3×v1+m×v2
Or, 12=3v1+mv2-------(1)
For perfectly-elastic impact,

Or, v2−v1=u1−u2=4m/s------- (2)
Conservation of kinetic energy gives

Or,

From equation (2), v1=v2−4
Substituting in equation (1),
12=3(v2−4)+mv2

Substituting in equation (3)

On solving, we get
m = 1,9
Therefore, possible values of m are 1 kg and 9 kg.

QUESTION: 54

The derivative of f(x) = cos(x) can be estimated using the approximation The percentage error is calculated asThe percentage error in the derivative of f(x) at x = π/6 radian, choosing h = 0.1 radian, is

Solution:

f(x) = cos(x)

So,

*Answer can only contain numeric values
QUESTION: 55

The aerodynamic drag on a sports car depends on its shape. The car has a drag coefficient of 0.1 with the windows and the roof closed. With the windows and the roof open, the drag coefficient becomes 0.8. The car travels at 44 km/h with the windows and roof closed. For the same amount of power needed to overcome the aerodynamic drag, the speed of the car with the windows and roof open (round off to two decimal places), is ________km/h (the density of air and frontal area may be assumed to be constant).

Solution:

The power needed to overcome the aerodynamic drag is given by Fd×V
Where, ���� is the drag force given by

For the power to remain same in both the cases of windows closed and open, then

Or,

Or, 0.1×443=0.8×V3
Or V = 22 km/h

*Answer can only contain numeric values
QUESTION: 56

An idealized centrifugal pump (blade outer radius of 50 mm) consumes 2 kW power while running at 3000 rpm. The entry of the liquid into the pump is axial and exit from the pump is radial with respect to impeller. If the losses are neglected, then the mass flow rate of the liquid through the pump is ________ kg/s (round off to two decimal places).

Solution:

Now, power = mass flow rate × u2
2000=m×(15.71)2
Or, m=8.106

QUESTION: 57

The Klein's method of construction for reciprocating engine mechanism

Solution:
*Answer can only contain numeric values
QUESTION: 58

Three sets of parallel plates LM, NR and PQ are given in Figures 1, 2 and 3. The view factor FU is defined as the fraction of radiation leaving plate I that is intercepted by plate J. Assume that the values of FLM and FNR are 0.8 and 0.4, respectively. The value of FPQ (round off to one decimal place) is ___________.

Solution:

*Answer can only contain numeric values
QUESTION: 59

Hot and cold fluids enter a parallel flow double tube heat exchanger at 100oC and 15oC, respectively. The heat capacity rates of hot and cold fluids are Ch = 2000 W/K and Cc = 1200 W/K, respectively. If the outlet temperature of the cold fluid is 45oC, the log mean temperature difference (LMTD) of the heat exchanger is ________ K (round off to two decimal places).

Solution:

Using the energy balance equation for the heat exchanger

QUESTION: 60

A differential equation is given as

The solution of the differential equation in terms of arbitrary constants C1 and C2 is

Solution:

Given differential equation
(D(D − 1) − 2D + 2)y = 4 where x = ez
Auxiliary equation, (D − 2)(D − 1) = 0
D = 1,2

*Answer can only contain numeric values
QUESTION: 61

Water flowing at the rate of 1 kg/s through a system is heated using an electric heater such that
the specific enthalpy of the water increases by 2.50 kJ/kg and the specific entropy increases by
0.007 kJ/kg.K. The power input to the electric heater is 2.50 kW. There is no other work or heat
interaction between the system and the surroundings. Assuming an ambient temperature of 300
K, the irreversibility rate of the system is _________kW (round off to two decimal places).

Solution:

The entropy generation (Sgen) is given by rise in entropy rise of the system (Since no heat interaction is involved)
So, entropy generation (Sgen) = m × specific entropy = 1 × 0.007 = 0.007 kW/K
Now, according to Gouy Stodola theorem,
Irreversibility =To × Sgen = 300 × 0.007 = 2.1kW

*Answer can only contain numeric values
QUESTION: 62

In an orthogonal machining with a single point cutting tool of rake angle 10o, the uncut chip
thickness and the chip thickness are 0.125 mm and 0.22 mm, respectively. Using Merchant’s
first solution for the condition of minimum cutting force, the coefficient of friction at the chip-tool
interface is ___________(round off to two decimal places).

Solution:

uncut chip thickness (t) = 0.125 mm
Cut chip thickness (tc) = 0.22 mm
So, ship thickness ratio
Rake angle (α) = 10°

Or shear angle (Ø) = 31.82°
According to Merchant’s theory, we have

So, β=90°−63.64+10=36.36°
Now, tanβ=µ (coefficient of friction)
Therefore, coefficient of friction = tan36.36°=0.74

*Answer can only contain numeric values
QUESTION: 63

An air standard Otto cycle has thermal efficiency of 0.5 and the mean effective pressure of the cycle is 1000 kPa. For air, assume specific heat ratio γ = 1.4 and specific gas constant R = 0.287 kJ/kg.K, If the pressure and temperature at the beginning of the compression stroke are 100 kPa and 300 K, respectively, then the specific net work output of the cycle is ___________kJ/kg (round off to two decimal places).

Solution:

Given data
P1 = 100kPa, T1 = 300K, mep = 1000 kPa, y=1.4, efficiency(η)=0.5, R = 0.287 kJ/kg-K
Using P1V1 = RT1

Efficiency(η)  where, r is the compression ratio = V1/V2

Or, r = 5.657
V1/V2 = 5.657
⟹V2=0.1522 m3/kg
Swept volume = V1 – V2 = 0.861 – 0.1522 = 0.7088 m3/kg
Went = Swept volume ×mep = 0.7088 × 1000 = 708.8 kJ/kg

*Answer can only contain numeric values
QUESTION: 64

A through hole is drilled in an aluminum alloy plate of 15 mm thickness with a drill bit of diameter 10 mm, at a feed of 0.25 mm/rev and a spindle speed of 1200 rpm. If the specific energy required for cutting this material is 0.7 N.m/mm3, the power required for drilling is _________W (round off to two decimal places).

Solution:

Specific energy = 0.7 Nm/mm3
So, power required for drilling= 0.7×125π=274.89W

*Answer can only contain numeric values
QUESTION: 65

A horizontal cantilever beam of circular cross-section, length 1.0 m and flexural rigidity EI = 200 N.m2 is subjected to an applied moment MA = 1.0 N-m at the free end as shown in the figure. The magnitude of the vertical deflection of the free end is _____________mm (round off to one decimal place).

Solution:

When the cantilever beam is subjected to moment at the free end, then the deflection at the free end is given by