COMBINED COMPETITIVE EXAMINATION (MAIN)
MECHANICAL ENGINEERING Paper-I Time 3 hours Full Marks 200 Note: The figures in the right-hand margin indicate full marks for the questions.

Attempt five questions in all.


Question No. 1 is compulsory.


1. Answer any ten of the following 4x10=40
What is cam? What type of motions can be generated'through the cam-follower mechanism?
Define open and closed loop controls along with some examples.
What is ductility and how is it measured?
Write the appropnate relations among the elastic constants used to determine the deformations produced in materials under the action of stress systems.
State the distortion energy theory used condition of a material under loading. for checking the failure
What are the mechanical properties that can be material by alloying it with some other materials? improved in a
Draw and planes in cubic face-centred cubic structure of materials. cells in the case of
Explain the importance of non-conventional machining processes.
What are the important factors economics of machining? to be considered in analysing the
Describe the main· phases of production planning and control.

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Discuss the measurement and process of capacity planning.
Draw a flowchart showing the grouping of a set of m items based their colours-red, black and white.
2. Answer any five of the following 8x5=40
A flywheel fitted to a steam engine has mass of 800 kg and radius of gyration of 360 mID. The starting torque of the engine is 580 Nm and it may be considered to remain constant throughout. Determine the kinetic energy stored in the flywheel after 12 seconds from the starting of the engine.

A thL"l cylindrical tank of length i and inner diameter d is fabricated with plates of thickness t. If the tank is to carry a gas under a uniform intelnal pressure of derive the circumferential and longitudinal stresses to be developed in it.


A solid circular steel disc of uniform thickness and 900 mm diameter rotates about its axis at 3000 r.p.m. The density and Poisson's ratio of the disc material are 7800 kg/m3 and respectively. Determine the radial and circumferential stresses at the centre and outer radius of the disc.


How many basic three-dimensional crystal are there? Write their names along with the Bravais space lattices belonging to them.


Explain the benefits of total quality control.


Write a complete C programming code for sorting an array of m numerical data in ascending order.
3. Answer any five of the following: 8x 5=4Q
Each arm of a Porter governor is 250 nun long. The upper and lower arms are pivoted to links of 40 mm and 50 mm respectively from the axis of rotation. The mass of each ball is 5 kg and that of the sleeve is 50 kg. The friction force on the sleeve is 40 N. Determine the range of speed of the governor for extreme radii of rotation of 125 mm and 150 mm.
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In a single-cylinder reciprocating engine, the mass of the reciprocating parts is 40 kg and that of the revolving parts is 30 kg at the crfu"1k radius. The speed of the crank is 150 r.p.m. and the stroke length of the piston is 350 mm. If 60% of the reciprocating parts and 100% of the revolving parts are to be balanced, determine the balance mass required at a radius of 320 mm.


In a single-degree damped vibrating system, a suspended mass of 8 kg makes 30 oscillations is 18 seconds. Determine the required damping coefficient so as to reduce the amplitude of vibration to 0·25 times of its initial value in 5 seconds.


The crank and connecting rod of a vertical petrol engine, running at 1800 r.p.m., are 60 mm and 270 mm respectively. The diameter of the piston is 100 mm and the mass of the reciprocating parts is 1-2 kg. During the expansion stroke if the gas pressure is recorded to be 650 N/m2 when the crank turns 20° from the top dead centre, determine the net force on the piston.


Two parallel shafts 3·5 m apart are connected by an open be1t-drive.The belt weighs kg per metre length. The two pulleys attached to the two shafts have diameters of 1000 mm and 400 rom, the larger pulley being the driver runs at 220 r.p.m. Owing to slip on one of the pulleys, the velocity of the driven shaft is 520 r.p.m. only. The maximum tension in the belt is not to exceed 1·8 kN. The coefficient of friction between the pulley material and belt is 0·28. Determine the efficiency of the drive.


Two mating gears have 30 and 50 numbers of involute teeth of module 100 mm and pressure angle 20° (the smaller gear is the driver). The addendum is one module. If interference is occurred in the system, determine a new pressure angle so as to eliminate interference.


4. Answer any four of the following 10x4=40

In order to ensure air-tight joint in a pressure vessel, hot riveting is employed at 250°C temperature with mild steel rivets of 20 nun diameter. If the length of a rivet is measured to be 30 mm immediately after riveting, estimate the change in length of a rivet and the stress induced in it upon cooling the joint to 30°C tempe:r:ature. The modulus of elasticity and coefficient of thermal expansion for steel may be taken as 210 GPa and 6·5 J..tm/{m. 0c) respectively.


A simply supported beam of 120 mm breadth, 180 mm depth and 6 m length carries a uniformly distributed load of 4 kN/m over its entire length. Compute the maximum shear stress developed in the beam.


A tubular steel strut pin-joined at both the ends has its inner and outer diameters of 40 mm and 50 mm respectively. Determine for what length of the strut the Euler's formula for buckling will cease to apply. For steel, 200 GPa as the modulus of elasticity and 3·3 GPa as the yield stress in compression may be taken.


A solid circular shaft is to transmit a mechanical power of 1590 Nm. Determine the required diameter of the shaft if the shearing stress is not to exceed 40 MPa and the angle of twist is limited to 6° over a length of 3 m. The modulus of rigidity of the shaft material is 83 GPa.


A load of 1000 N is dropped axially on a close coiled helical compression spring from a height of 250 mm. The wire diameter of the spring is 20 mm and its modulus of rigidity is 84 GPa. The spring index is 8 and it has 20 active coils. Determine the deflection and stress induced in the spring.


A propeller shaft is to transmit a twisting moment of 100 kNm and an axial thrust of 250 kN. the propeller is fitted very close to the bearing so that the bending effect can be neglected. The internal and external diameters of the shaft are 180 mm and 250 mm respectively. Determine the maximum values of the induced compressive and shear stresses.


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5. Answer any four of the following 10x4=40

Show that the atomic packing factor in the body-centre cubic structure of a crystalline material is -J3n /8.


Classify point imperfections in crystalline materials with sketches and short description.


State with some examples the advantages of using aluminium alloys and nickel alloys over their pure forms.


Explain various possible stages in a binary phase diagram of alloying.


State the improvements in steel that can be achieved through heat treatment.


In a fibre-reinforced composite material, Ef and Vf are respectively the modulus of elasticity and volume fraction of the fibre, while those of the matrix are Em and Vm respectively. Derive the modulus of elasticity of the composite during transverse loading under general assumptions.


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6. Answer any four of the following: 10x4=40

Describe the important characteristics of sheet metals that have significant effects on forming operations.


Using the Taylor's tool life 'equation with 0·5 as the exponent term in the equation that depends on tool and workpiece materials and cutting conditions, calculate the percentage increase in tool life when the cutting speed is reduced by 50%."


What does automation in machining mean? Explain the differences between hard and soft automations in machining.


Explain the principle and capabilities of the electrochemical machining process.


Explain what is meant by machinability and what it involves? Why does titanium have poor machinability?


Explain why cutting force increases with depth of cut and decreases with rake angle.


7. Answer any four of the following 10x4=40

What is break-even analysis? The ABC Company has a demand for supplying 130000 units of a new product. Three potential locations Y and Z are available with fixed cost and variable cost per unit as ($150000, ($350000, and ($950000, respectivelyJdentify which location is to be selected.


A company needs to assemble cars through a certain number of steps as listed below with their priority relationship


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Code of Task Title Task Time Prerequisite
task (seconds) Tasks
A Position rear axle support and hand fasten 45
B Four screws to nuts 11 A
C Insert rear axle 9 B
D Tighten rear axle support screws to nuts 50
E Position front axle assembly and hand fasten 15 D
F Fasten four screws to nuts 12 C
G Tighten front axle assembly screws 12 C
H Position rear wheel 1 and fasten hubcap 12 E
I Position rear wheel 2 and fasten hubcap 12 E
J Position front wheel 1 and fasten hubcap 8 I
K Position front wheel 2 and fasten hubcap 9 J


Determine the minimum time required to complete the assembly of car.

A manufacturing company is to purchase 9000 parts of a machine as its annual requirement ordering monthly-basis at a time. Each part costs the ordering cost per order is $15 and carrying charges are 15% of the average inventory per year. Based on EOQ model of inventory control, suggest a more economical purchase policy for the company showing the savings from the suggestion.


What are the objectives of material requirement planning? Discuss various inputs and output§ of the material requirement planning system.


Describe various graphical methods used to control the quality of a product.


A company manufactures two machines, A and B. Using available rel:>ources, either 28 A or 14 B machines can be manufactured daily. The sales department can sell up to 14 A machines or 24 B machines. The shipping facility can handle no more than 16 machines per day. The company makes a profit of $400 on each A machine and $600 on each B machine.· How many A and B machines should the company manufacture everyday to maximize its profit?


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8.
Prove that the surfaces containing the maximum shear stresses and those containing the principal stresses are at ±45° angle apart. A vertical plane of a body is under the action of a tensile stress of 80 MPa along with a clockwise shear stress of 50 MPa. Determine the two-dimensional principal stresses and their directions.

9.
What is four-bar mechanism? What is its importance? A four-bar mechanism is represented by a quadrilateral ABCD, in which AD is fIxed. The crank AB rotates in a clockwise direction at 120 r.p.m. speed and drives the link CD by means of the connecting link Be. Determine the angle through which CD oscillates and its angular velocity in one of the positions when BC is perpendicular to AB. The lengths of AB, BC, CD and AD are 75 mm, 350 mm, 12S mm and 400 mm respectively. 40


40

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