# MPPSC Question 2017 Paper- I

(A) A hollow circular bar of outside diameter  twice the  inside  diameter  is used as a beam. The bar is subjected to bending moment of 40 kN m. If the allowable bending stress in the beam is to be limited to 100 MN/m 2 , find the inside diameter of the bar.

(B)Make a list of six principal theories of failure. Explain major consideration and  application  of maximum  principal stress theory.

(C)A flat bar 32 mm wide and 12 mm thick is loaded by a steady tensile load of 85 kN. The material is mild steel with yield point stress of 315 N/ mm2 .Find  the  factor  of safety based  on the yield point.

(D)Design the longitudinal joint for a 1-25 m diameter steam boiler carrying a steam pressure of 5  N / mm‘. The allowable  stress of  the  plate  material  is 80 N / mm 2 in tension. Length of the shell of boiler is 5 m. Take allowable stress for  shielded  arc  weld = 95  N / mm 2 .

(E) Find the length of belt (open and cross) necessary to drive a pulley of 80 cm diameter running parallel at a distance of 12 m from  the  driving  pulley  of diameter  480 cm.

(F)Make a list of various types of gear trains. Derive an expression for ve1ocity ratio  of  a  simple gear train.

(G)A uniform  disc of  diameter  30 cm  and  weighing  5  N is  mounted  on one end of an arm of length 60 cm. The other end of the arm is free  to  rotate  in a universal   bearing.   If   the     disc   rotates   about   the   arm   with   a   speed   of 300  r.p.m. clockwise, looking from the front, with wb.at speed will it precess about  the vertical axis ?

(H) For  what  type  of  materials  ultrasonic  machining  (USM)  is  best  suitable process of material removal ?  Make  a  sketch  showing  major  parts  of  USM setup.

(I) Classify comparators. Explain the working and constructional details of any one comparator.

(J) For a small project with five jobs, the following data is given :

 JOB Immediate Predecessors Duration (days) Mean STD. deviation A - 10 2 B - 5 1 C A 16 2 D A 12 2 E B,C 15 1

(i)
Draw the project network in activity on arc mode.

(II)     Under   PERT   assumptions,   determine   the    distribution    of    project duration.

SECTION   A

## (A) A short column of I-section 25 cm x 20 cm has cross-section Sea of 52 cm2 and maximum radius of gyration 10-7 cm. A vertical load in kN acts through the centroid of the section together with a parallel load of in /4 kN acting through a point on the centreline of the web distant 6 cm from the centroid. Calculate the greatest allowable value of in if the maximum  stress is not to exceed 65 MN/ m 2. What is then the minimum stress ?(B) A close-coiled helical spring is to have a stiffness  of  900  N/m  in compression, with a maximum load  of  45  N  and  a  maximum  shearing stress of 120 N / mm 2. The solid length of the spring (i.e., coils touching) is 45 mm. Find the(I)   wire diameter;(II)  mean coil radius;(III) number of coils.Take  modulus  of  rigidity  of  material  of  the   spring  = 0-   4 x 10 5  N / mm 2.(C) A simple band brake. is applied to a drum of 560 mm diameter  which rotates at 240 r.p.m. Angie of contact of the band is 270‘. One end of the band is fastened to a Fix pin and the other end to the brake lever 140 mm from the fixed pin. The brake lever is 800 mm long and is placed perpendicular to the diameter that bisects the angle of contact. Assuming the coefficient of friction as 0 3, determine the necessary pull at the end of the lever to stop the drum if 40 kW of power is being absorbed. Also, find the width of the band if its thickness is 3 mm and the maximum tensile strength is limited to 40 N /mm2. 3. (A) A V-belt of 6-0 cm 2  cross-section has  a groove angle of 40°  and  an angle of lap   of  150°,  µ= 0-   10.  The   mass  of  the   belt  per  meter  run  is  1-2 kg.  The maximum  allowable  stress in the belt is 850  N /cm   2 .  Calculate  the horse- power that can be transmitted  at  a  belt speed  of   30 m/s.(B) Derive  an  expression  for maximum and     minimum values of swaying couple.(C) A V-twin engine has the cylinder axis at right angles and the connecting rods operate a common crank. The  reciprocating  mass  per  cylinder  is 1-5 kg and the  crank radius 75 mm. The length  of  the  connecting  rod is 0 3 m. Show that the engine may be balanced for primary forces by means of a revolving balance mass. If the engine speed is 500 r.p.m., what is the value of the maximum resultant ,secondary force ?                               SECTION—B                   Attempt at least one question4.(A) Design the rectangular key for a shaft of 50.mm  diameter. The shearing and crushing stresses for the key material are 42 MPa and 70 MPa, take w = 16 mm and t = 10  mm, where in = width and t = thickness of the key.(B) Design a cast iron protective type flange coupling  to transmit  15 kW at 900 r.p.m. from an electric motor to a compressor. The service factor may be assumed  as  1. 35. The following  permissible  stresses  may be  used :      Shear stress for shaft, bolt and key material = 40 MPa Crushing stress for bolt and key = 80 MPaShear stress for cast iron = 8 MPa (C) The following data relate to a shaft held in long bearings :Length of the shaft =1.2 mDiameter  of  the shaft = 14  mm Mass of a rotor at midpoint = 16kgEccentricity of centre of mass of rotor from centre of rotor = 0.4  mmModulus of elasticity of the shaft material = 200 GN / m2               Permissible stress in the shaft material = 70 x 106 N / m2Determine  the  critical  speed  of the  shaft.5(A) A steel rod is turned with a single-point cutting tool having rake angle 10°. The chip thickness was measured as 1-5 mm. The dynamometer gave indication of cutting forces as 980 N for tangential component and 440 N for thrust component, compute friction force at chip tool interface and shear strength of the material (assume uncut chip thickness as 0-6 mm and uncut width of chip as 1-8 mm). (B) During straight turning of 25 mm diameter steel bar at 300 r.p.m. with HSS tool, a tool life of 10 minutes was obtained. When the same bar was turned at 250 r.p.m., the tool life increased to 52-5 minutes. What will be the tool life at a speed of 275 r.p.m?(C) Comment on the following statements related to electrochemical machining (ECM) ;(i) "ECM is reverse of electroplating."(II) "AC power supply cannot be used in ECM."(III) "Tool wear in ECM does not involve material loss."(iv) "ECM is a hi^ly predictive process of material removal."(D) Write any five differences between traditional and non-traditional machining processes.                                        Section—C                          Attempt at least one question6. (A) A company uses the purchased item continuously in the manufacturing of a large number of products. The item has the following characteristics :Demand/year = 8000 PcPurchase price = f 100/PcSafely stock = 1 • 6 x lead time demandLead time from order to delivery = 4 weeksPurchasing quantity = 1000 PcInventory carrying cost/year = 20% of the item valueA reorder point system that continuously reviews stock on hand is used to generate purchase orders. The product is produced and in demand in all 52 weeks of the year :(I) Determine the reorder point, the average tied-up capital in inbound stock, the inventory turnover rate in the stock, the average run-out time in the stock and the annual inventory carrying cost for the item.(II) As the company buys several items from the same supplier it is considering changing its review principle from continuous review to periodic review stock on hand of all purchased items every second week. By doing this, it is thought that it will be possible to coordinate deliveries of several items from this supplier. How will the answer in (i) change if a switch is made to periodic review?  (B) A company makes two types of leather belts, A and B. Belt A is high quality belt and belt B is of lower quality. The respective profits are f 4 and f 3 per belt. Each belt of type A requires twice as much time as belt of type B, and if all the belts were of type B, the company could make 1000 per day. The supply of leather is sufficient for only 800 belts per day (both A and B combined). Belt A requires a fancy buckle and only 400 per day are available.There are only 700 buckles a day available for belt B. What should be the daily production of each type of belt? Formulate as a linear programming problem (solution not required).(C) The following table shows the jobs of a network along with their time estimates (in days) : (i) Draw network diagram.(ii) Find critical path. Also, find the expected duration of the project.(Hi) Calculate the standard deviation of the project length.(iv) Find the probability that the project is completed in 31 days

7. (A) Calculate the fundamental deviation and tolerances and hence the limits of size for the shaft and hole for the following fit :

60 mm H7-f8

The diameter steps are 50 mm and 80 mm.

(B) A television repairman finds that the time spent on his jobs has an exponential distribution with a mean of 30 minutes. If he repairs sets in the order in which they came in, and if the arrival of sets follows a Poisson's distribution approximately with an average rate of 10 per 8-hour day, what is the repairman's expected idle time each day? How many jobs are ahead of the average set just brought in?

(C) A cantilever member 0-1 m long having cross-section of 0-05 mxO-25 m supports a load of 27.5 kN. What is the maximum shear stress and where does it occur?