A beam AB of length 2 m. hinged at A and supported at B by a cord which passes over two frictionless pulleys carries a 50 kN load as shown in Fig. Determine the distance where 100 kN load is located on the beam, if the beam is to remain in equilibrium in horizontal position. Also determine the reaction at the hinged end.

<img src='./qimages/15693-1a.jpg'>

A state of plane stress is shown in Fig.
Determine the following

Principal stresses

Principal planes

Maximum shear stress

<img src='./qimages/15693-1b.jpg'>

A thin spherical vessel of 1000 mm diameter and 2 mm thickness is subjected to an internal pressure of 4 MPa. The Young's modulus and Poisson's ratio are 200 GPa and 0·3 respectively. Find the following

Hoop stress

Change in volume of the vessel 10

A steam engine develops 300 kW power at 9·5 rad/s. The coefficient of fluctuation of energy is found to be and fluctuation of speed is kept within of mean speed. Find the mass of the flywheel required if the radius of gyration is 2 m.

A machine of mass 8 kg is supported on springs having combined stiffness of 5.4 N/mm. A dashpot is attached to the system that exerts a force of 40 when the mass has a velocity of 1 m/s. Determine the following

Critical damping coefficient

Damping factor

Logarithmic decrement

Ratio of two consecutive amplitudes

A simply supported beam of rectangular section is 200 mm wide and 300 mm deep. It supports a uniformly distributed load of 6 kN/m over an effective span of 4 m as shown in Fig.2.(a) Calculate the magnitude and direction of the principal stresses at a point located at 0·50 m from the left support and 50 mm above the neutral axis.

<img src='./qimages/15693-2a.jpg'>

Compare the permissible diameter of a steel circular shaft, subjected to torsion, according to the following theories of failure. Assume Poisson's ratio to be 0·3

Maximum stress theory

Maximum shear stress theory

Maximum strain theory

Fig. shows three fiat blocks positioned on the 30° incline. A force P parallel to the incline is applied to the middle block. The movement of the upper block is prevented by attaching to a fixed support by a wire. The coefficient of static friction for each of the three pairs of mating surfaces is shown in the figure. Determine the maximum value which P may have before any slipping takes place.

<img src='./qimages/15693-2c.jpg'>

A solid aluminium shaft 1 m long and 50 mm diameter is to be replaced by a tubular steel shaft of the length and the same outside diameter (i.e. 50 mm) such that each of the two shafts could have the same angle of twist per unit torsional moment over the total length. What must the inner diameter of the tubular steel shaft be? The modulus of rigidity of steel is three times that of aluminium.

A compound epicyclic gear is shown in Fig. Gears D and E are free to rotate on axis P. Compound gears B and C rotate together on axis Q at the end of arm F. All the gears have equal pitch. The number of external teeth on gears B and Care 18, 45 and 21 respectively. Gears D and E are annular gears. Gear A rotates at 100 r.p.m. in counter-clockwise direction and gear D rotates at 450 r.p.m. clockwise. Find the speed and direction of arm F and gear E.

<img src='./qimages/15693-3b.jpg'>

For a eutectoid steel, draw and label continuous cooling transformation diagram. Explain normalizing and hardening heat treatment with regard to phase transformation using relevant cooling curves on CCT diagram.

Four masses C and D are attached to a shaft and revolve in the same plane. The masses are 12 kg, 10 kg, 18 kg and 15 kg respectively and their radii of rotation are 40 mm, 50 mm, 60 mm and 30 mm respectively. The angular positions of masses C and D are 135° and 2700 from the mass A. Find the magnitude and position of balancing mass at a radius of 100 mm.

Draw the stress-strain diagram for mild steel and describe the salient points of the curve.

A Porter governor having all arms of 240 mm length is pivoted on the axis of rotation. Each ball has a mass of 5 kg and the load on the sleeve is 18 kg. The ball path is 150 mm when the sleeve begins to rise and 200 mm at the maximum speed. Find the following

Range of speed

Coefficient of sensitiveness, if the friction at the sleeve is equivalent to a force of 10 N

Electrochemical machining of 400 mm^2 surface of iron is performed using supply voltage of 15 V and tool-workpiece gap of 0·3 mm. Considering gap resistance for the flow of current through electrolyte to be 0·0015 ohm, calculate the metal removal rate, MRR
The relevant data for iron are the following
Valency 2
Atomic weight 55·85
Density 7860 kg/m^3
Faraday's constant 96540 coulombs

An annealed copper plate of 300 mm width and 20 mm thickness is rolled to 16 mm thickness in one pass. Considering radius of the roller as 400 mm, rotational speed of 80 r.p.m. and average flow stress during rolling as 400 MPa, calculate the true strain and rolling force

The machining of steel is carried out using two types of cutting tool, Le., tool A and tool B. Data/technical parameters related with tools are given below in the table. Which tool will you prefer for 200 minutes of tool life and why?

Tool Value of n for tool life equation Cutting speed for one minute tool life

Tool A 0·25 150
Tool B 0·30 180


Describe the philosophy of lean management including waste and value stream with regard to manufacturing.

The demand for an item is 500 units and 600 units for July and August respectively. Considering forecast for July as 300 units, determine the forecast for September using exponential smoothing method. Assume value of a as 0·3.

For orthogonal turning using a cutting tool having a rake angle of the following data is given

Chip-thickness ratio 0·5
Rake angle 5°
Main cutting force 1600 N
Thrust force 1300 N
Calculate the shear plane angle, friction force normal force and
coefficient of friction at chip-tool interface.

Two aluminium plates are welded using tungsten inert gas welding process with the help of welding current 150 arc voltage 12 V and arc travel speed 2 m/s. Considering heat transfer efficiency of TIG welding process as 90% and heat required for melting unit volume of metal as 15 J/mm^3
calculate the melting efficiency of the process if the cross-sectional area of the weld joint is 20 mm 2.

Explain the principle of abrasive waterjet machining using suitable schematic. Write the advantages and applications of abrasive waterjet machining.

The following limits are specified to give a clearance fit between a shaft and a hole in a limit system


Shaft 30-0.021
+0·023
Hole 30-0 ,000

Calculate the following

Basic size

Shaft and hole tolerances

Shaft and hole limits

Maximum and minimum clearances

Lathe machine operations take 40 min to produce a product. If the efficiency of the lathe machine is 80% and rejection is then determine the number of lathe machines required for producing 800 pieces per week. Assume 52 weeks per year and 48 hours per week as working hours available.

A manufacturing company is producing an item for which the following information is given
Selling price per unit Rs 20
Variable cost per unit Rs 10
Fixed cost Rs 2,00,000
However due to changing market condition, variable cost increased by 20% and fixed cost increased by 10%. If the breakeven quantity is maintained, then what will be the revised selling price?

Monthly consumption of an item is 350 units and price per unit is Rs 15. Inventory carrying cost is 20 percent and ordering cost is Rs 40 per order; lead time of 1 month's stock. Assuming ROL system, calculate the following:

Reorder quantity

Reordering level

Minimum level

Maximum level

Average inventory

A car manufacturer performs final inspection before shipping to the dealers. The final inspection involves testing and inspection of car with regard to number of parameters. There is a possibility that a car may fail to satisfy various parameters (which can be termed as defects). Periodically ten cars were taken randomly for testing and inspection. Data obtained after inspection and testing of each car with regard to number of defects is given below. Determine the control limits for C chart and comment

Sample/Car 1 2 3 4 5 6 7 8 9 10
No. of defects 10 12 13 08 09 10 12 20 07 06

Describe different types of control systems possible for CNC operations along with respective applications using suitable schematic.