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MECHANICAL ENGG. DEPT SEMESTER #2

APPLIED - 3300008 UNIT 1: INTRODUCTION 1. Differentiate: 1) Vector quantity and Scalar quantity 2) and 2. State SI system unit of following quantities: 1) Density 2) Angle 3) 4) 5) 6) Pressure 7) 8) 3. Name the type of quantities: 1) Density 2) 3) Work 4) 5) Force 6) 7) Velocity 8) UNIT 2: COPLANAR CONCURRENT 1. Explain principle of super position of forces. 2. Explain principle of transmissibility of forces. 3. State and prove lami’s theorem. State its limitation. 4. Explain polygon law of forces. 5. Classify forces. 6. State and Explain law of parallelogram of forces. 7. State and Explain law of triangle of forces. 8. The system shown in figure-1 is in equilibrium. Find unknown forces P and Q. 9. Find magnitude and direction of resultant force for fig.2

Fig.1 Fig. 2 Fig.3 Fig.4

10. A load of 75 KN is hung by means of a rope attached to a hook in horizontal ceiling. What horizontal force should be applied so that rope makes 60o with the ceiling?

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MECHANICAL ENGG. DEPT SEMESTER #2

11. The boy in a garden holding two chains in his hand which are Hooked with Horizontal steel bar making an angel 65° & other chain with an angle of 55° With the steel bar, if the weight of boy is 55 kg, than find tension developed in both chain. 12. A circular sphere weighing 500 N and having a radius of 200mm hangs by a string AC 400 mm long as shown in Figure 3. Find reaction offered by the wall and tension in the string. 13. A Body weighing 2000 N is suspended from a vertical wall by a string AB 2m long as shown in fig.4. It is pulled by a horizontal force of 320N. Find tension (T) in the string AB and lateral (x) of the body.

UNIT 3: COPLANAR NON-CONCURRENT FORCES 1. Define: 1) Force 2) 3) 2. State conditions of equilibrium of coplanar non-concurrent, non-parallel forces. 3. Explain different types of load and supports of beam. 4. State varignon’s principle of moment. 5. Find the support reactions for a beam shown in figure 1. 6. Find resultant for the system of forces shown in figure 2. Also find couple moment at the centre. 7. Find support reactions for a beam shown in figure 3. 8. Find support reactions for beam shown in fig. 5 9. Find resultant and its direction for forces given in fig.4 10. Find magnitude, direction and position of resultant force for a given system (shown in fig.6) of force acting on body.

Fig.1 Fig. 2

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MECHANICAL ENGG. DEPT SEMESTER #2

Fig.3 Fig. 4

Fig. 5 Fig. 6

UNIT 4: CENTRE OF 1. Define: 1) Centroid 2) Centre Of Gravity 3) Moment 2. Find centroid for the lamina shown in fig 4. 3. Find center of gravity for the lamina shown in fig 1. 4. Find centroid for the lamina shown in fig 2. 5. Find centroid for the lamina shown in fig 3. 6. Find centroid for the lamina shown in fig 5. 6. Find centroid for the lamina shown in fig 6.

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MECHANICAL ENGG. DEPT SEMESTER #2

Fig.1 Fig.2

Fig.3 Fig.4

Fig.5 Fig.6

UNIT 5: 1. Define friction and state the law of friction. 2. Define: 1) angle of friction 2) Angle of repose 3) Co-efficient of friction 3. Explain types of friction. List advantages and disadvantages of friction.

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MECHANICAL ENGG. DEPT SEMESTER #2

4. A body of weight 8 KN is lying on a rough inclined plane at an angle of 30o with horizontal. If the angle of friction is 25 o, find the minimum effort parallel to the plane required just to support the body. 5. A ladder weighing 400N is 10m long. Its end ‘A’ is resting on smooth vertical wall and lower end ‘B’ is resting on rough horizontal floor having coefficient of friction is 0.4. The ladder makes an angle 45 o with horizontal. The ladder is about to slip when a man weighing 600N standing at mid length of the ladder. Find reactions at supports A and B and limiting friction at the floor. 6. Find horizontal force required to push a body weighing 20kN up a ramp inclined 30 o with horizontal. Take friction coefficient. = 0.25 7. A block weighing 360N rests on a rough horizontal floor. A force of 120 N inclined at 60o with the floor is just sufficient to move it. Find co efficient of friction between floor and block.

UNIT 6: WORK, POWER AND ENERGY 1. Define: 1) Work, 2) Power 3) Energy 4) 5) 2. Explain law of conservation of energy. 3. Find out the power required to lift a load of 15000 kg at a height of 20 mm within 10 minute time. 4. A train weighing 600 KN runs at a speed of 36 KMPH. Calculate Kinetic Energy of the train. 5.Water is to be lifted from a ground tank 7.5mt deep in tank 2.5m x 2.5m x1.5m located at 11.5mt high from ground in 45 minutes Calculate the required power of the Pump in watt. 6. A water tank having capacity of 25,000 litres is to be filled up in 30 minutes. The water is to be lifted through a height of 20 metres. Find power of a pump in kW required to fill the tank if pump's efficiency is 75% . 7. A train weighing 2000 kN is pulled on a level track at constant speed of 45 km/hr by an engine. If frictional resistance is 10 N/kN, calculate horse power of the engine.

UNIT 7: SIMPLE MACHINES 1. Define: 1) Mechanical Advantage 2) Velocity ratio 3) Input 4) Output 5) Efficiency 6) Ideal machine 2. Explain reversible and non reversible machine. 3. Explain law of machine. 4. A simple machine lifts a load of 50 KN by an effort of 10 KN. If the maximum mechanical advantage is 10. Calculate an effort required to lift a load of 120 KN. 5. Calculate maximum mechanical advantage and maximum efficiency of a machine having law of machine P = 1/20 * W + 135 and V.R. = 25. 6. The following results were obtain on single purchase crab winch having diameter of effort wheel 40cm that of load wheel 12.5cm, no. of teeth on spur wheel is 92 and that on pinion wheel is 20,From the

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MECHANICAL ENGG. DEPT SEMESTER #2

graph determine the law of machine, maximum efficiency and also find effort required to lift load of 550N. Load in N 250 375 450 650 800 Effort in N 75 125 225 350 425 7. A screw jack had a thread of 12mm pitch. What effort at end of a handle 500mm long will be required to lift a load of 3KN, if the efficiency at this load is 48%. 8. In a lifting machine a load of 20kN is lifted by an effort of 0.8Kn and a load of 40kN is lifted by an effort of 1.20kN. Find law of machine and efficiency at load 40kN & VR=40. 9. In a machine an effort of 1 kN raised a load of 8 kN. The Distance moved by the effort was 20 meters while that moved by the load was 1 metre. Find Mechanical advantage, Velocity ratio and efficiency of the machine.

SUBJECT: - 3321901(MD)

Unit 3:- Projection of solids

1. A square prism, edge/side of base 30mm and height 45mm, is resting on H.P. on the edges of the base. The edge on which it rests on H.P. makes 45° with V.P. the base of the prism makes 30° with H.P. or the axis of the prism makes 60° with H.P. or rectangular face containing the edge on which it rests on H.P. makes 60° with H.P. Draw the projections of the prism, when (a) base is away form the observer or nearer to V.P. (b) base is nearer to observer or away from V.P.

2. A cone, diameter of base 50mm and height 60mm,is resting on H.P. on a point of its periphery of base with the axis making an angle of 30° with the H.P. and the plan of the axis making 45° with the V.P. Draw the projections of the cone.

3. A cylinder, diameter of base 60mm and height 90mm, is resting on the H.P. on the point of its periphery of the base. The axis of cylinder is inclined to H.P. by 30° and the top view of the axis is inclined at 45° to the V.P. Draw the projections. Keep top end of the cylinder nearer to V.P.

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4. A hexagonal pyramid of base of the side 30mm long and altitude 60 mm is resting on one of its base edge on the H.P. This edge makes 30° to the V.P. and the face containing this edge makes 45° to the H.P. Draw the projections.

Unit 3:- Section of solids

1. A cone, base 50 mm diameter and 60mm height is resting on H.P. on its base. It is cut by a cutting plane perpendicular to both H.P. and V.P. and is 10mm away form the axis. Draw elevation, plan and sectional side view of the cone. State the nature of the section.

2. A cylinder of 55 mm dia., 70 mm height having its axis vertical, is cut by section plane perpendicular to V.P and inclined at 60° to H.P and intersecting the axis 35 mm above the base. Draw its front view and true shape of section.

3. A hexagonal prism of 25 mm. side of the base and 60 mm height is lying on the H.P. on one of its rectangular faces with the axis parallel to V.P It is cut by a cutting plane inclined at 45° to H.P and perpendicular to V.P cuts the axis of the prism at 20 mm from the end. Draw elevation, sectional plan and true shape of the section.

4. A hexagonal pyramid side of the base 25 mm and axis 55 mm long rests on its base on H.P Such that two of edges of its base are perpendicular to V.P., It is cut by a section plane perpendicular to H.P. and inclined at 45° to V.P and passing through the pyramid at a distance of 10 mm from the axis, Draw the sectional Front view and TRUE SHAPE of the section.

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MECHANICAL ENGG. DEPT SEMESTER #2 Unit 4:- Intersection of solid

1. A vertical square prism, base 60mm and axis length 110mm has its base in the H.P. and rectangular faces equally inclined to the V.P. It is penetrated by a horizontal square prism base 40mm side and axis length 110 mm. A rectangular face of the horizontal prism is inclined at 30º to the H.P. Draw their projections showing lines of intersection, when the axis of horizontal prism is parallel to V.P. and 5mm in front of the axis of vertical prism.

2. A vertical cone, diameter of base 75mm and axis 110mm long is resting on the H.P. on its base. A cylinder of 40mm diameter intersects the axis of the cone at right angle and 27mm above the base. The axis of the cylinder is parallel to both H.P and V.P. Draw the projections with showing lines of intersections.

3. A vertical cylinder of 50mm diameter and 80mm height is penetrated by a horizontal square prism of 25mm side and 70mm length. Their axis is perpendicular and intersecting each other. The faces of prism are equally inclined to H.P. and V.P. Draw the projections showing line of intersection. 4. A cone having base diameter 50mm and height 60mm is resting on H.P. It is penetrated by vertical cylinder of 30mm diameter and 70mm height from top. The axes of two solids are 6mm apart and parallel. The plane containing two axes is parallel to V.P. Draw the projections showing curves of penetration.

5. A cone, base 80mm and height 85mm resting on its base on H.P. is completely penetrated by a cylinder of Φ40 mm in such a way that its axis is parallel to V.P. and is 23 mm above the base of the cone and 6mm in front of the axis of the cone. Draw the projection of the solid showing curves of penetration.

6. A vertical cylinder, base 60mm diameter and height 70mm is resting on H.P. on its base. A horizontal hole of 50mm diameter is drilled through the vertical cylinder. The axis of the hole is parallel to V.P. and 10mm away from the axis of the vertical cylinder and is nearer to the observer. Draw the projections of cylinder showing hole. Page 8 of 27

MECHANICAL ENGG. DEPT SEMESTER #2

Unit 5:- Development of surfaces

Q.1 Draw the development of the lateral surfaces of the given cylinder.

45°

30°

Ø40 60

30°

Q.2 Draw the development of the lateral surfaces of a given prism.

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MECHANICAL ENGG. DEPT SEMESTER #2

45°

A

B

C R20

20

Q.3 Draw the development of the lateral surfaces of the given cylinder of 80mm diameter. 10 10

20

Ø40 40

20 10 10

Q.4 Draw the development of the given cone. Assume suitable data.

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MECHANICAL ENGG. DEPT SEMESTER #2

30° 70 40

R25

Ø50

Q.4 A hollow pyramid, side of base 45mm and height 65 mm, is resting on H.P. on its base with all sides of base equally inclined to V.P. A square hole of side 20 mm is drilled through the pyramid. Sides of the square hole are equally inclined to H.P. Axes of the pyramid and square hole intersect at right angle 20 mm above the base of the pyramid. Axis of the hole is perpendicular to V.P. Draw the development of the lateral surfaces of the pyramid.

65 20

20

Q.5 Draw development of lateral surface of truncated cylinder given in figure below.

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MECHANICAL ENGG. DEPT SEMESTER #2

45°

30°

R20 80

30

10

Ø50

Q.6 Draw the development of parts A, B, C & D shown in figure below.

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MECHANICAL ENGG. DEPT SEMESTER #2

Ø48

30° 25

8

Ø20

40

10

Ø50

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MECHANICAL ENGG. DEPT SEMESTER #2

Unit 6 & 7:- Welding, piping-symbols & surface roughness

Q.1 Draw welding symbols for following

1. Single bevel butt 9. Single V butt 2. Spot weld square butt 10. Seam 3. Single J butt 11. Double bevel butt weld 4. Plug 12. Backing run 5. Single U butt 13. Double U butt 6. Fillet 14. Double J butt 7. Stud 15. Double V butt 8. Stitch

Q.2 Two plates are to be welded by fillet weld. On other side of arrow welding fillet size is 6mm. First 30mm length to be welded and next 20mm not to be welded and so on. On arrow side fillet size is 5mm. First 20mm not to be welded and next 30mm to be welded and so on. Draw welding symbol indicating all details including field weld.

Q.3 Two plates are to be welded by Double U butt joint. On other side of arrow weld size is 5mm. First 30mm length to be welded and next 20mm not to be welded and so on. All sides are to be welded and on arrow side flush finishing is to be done. Draw welding symbol in corporating all details.

Q.4 Draw pipe fitting symbols for following.

1. Lateral 3. 45 Elbow 2. Globe valve 4. Cross

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MECHANICAL ENGG. DEPT SEMESTER #2

5. Safety valve 12. Gate valve 6. Nipple 13. Stop cock 7. Coupling 14. Check valve 8. Union 15. Eccentric reducer 9. Plug 16. Angle gate valve 10. Cap 17. Reducer 11. Tee 18. Angle globe valve

Q.5 Surface roughness symbol is shown in Fig. Explain the information covered on it.

Milled

15 2.5

2.0 =

Q.6 Draw surface roughness symbol incorporating following details.

1. Surface roughness limit 6.3 micron 2. Method used for surface GRIND 3. Sampling length 60mm 4. Direction of lay Circular 5. Machining allowances 2mm

Q.7 Draw surface roughness symbol which includes the following details.

1. Roughness value 10 micron 2. Production method Shaping 3. Allowance 3 mm 4. Type of lay Parallel Page 15 of 27

MECHANICAL ENGG. DEPT SEMESTER #2

Q.8 Draw surface roughness symbol following details.

1. Roughness value 10 micron 2. Production method Grinding 3. Machining Allowance 2 mm 4. Type of lay Circular

Q.9 Draw surface roughness symbol incorporating following details.

1. Surface roughness limit 12 µm 2. Method used for surface MILLED 3. Sampling length 25mm 4. Direction of lay Parallel 5. Machining allowances 2mm

Q.10 Draw surface roughness symbol and gives the details include on it.

Q.11 Draw the symbol for following.

1. Vacuum liner 5. Concentricity 2. Air line 6. Flatness 3. Refrigerant line 7. Lay symbol of weld 4. Perpendicularity

Q.12 Draw symbol of pipe carrying following fluids.

8. Gas 9. Oil 10. Hot water 11. Cold water

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Unit 8:- Assembly to details drawing

Q.1 An assembly drawing of “Knuckle joint” is shown in figure below. Draw detailed drawing of each part in two views using “First angle projection method”. Prepare part list.

Unit 8:- Details to assembly drawing

Q.1 Figure below shows the details of “Tool post”. Assemble the parts and draw following views of the assembly. Use first angle projection method.

(a) Front view (b) Top view

ASSIGNMENT

MATHEMATICS-II(3320002/3320003)(GROUP 1/GROUP 2)

CHE-1(COMPLEX NUMBER)

1.Find conjugate of complex number.

(1) ,(2)2+3i, (3)1+0i

2.Find absolute & squaroot of complex number & convert

In-to polar form.

(1)1+ , (2) , (3) 2+ i ,(4) 0+i

3.If z=x+iy and , show that ,when real & imagenary parts same, i.e a=b.

4.If z=a+ib and ,then prove that .

5. Simplify,

1.

2.

6.Find complex number z = x+iy.

1. If arg = and r = 4 2. If arg = and r = 2

Assingnment : - 2 CO-ORDINATE GEOMETRY

1.POINT : -

1.Find the distance between the following point.

1. (m and 2. and

2. Three vertices of the parallelogram ABCD are A ,B and C , find fourth vertex D.

3. Prove that the point A , B and C are collinear.

4. Find the value of x when A , B and C are the vertices of and B = 90 .

5. Find the locus of a point which moves such that its distance from the point is twice the distance from .

2.LINE : -

1.Find the equation of line which is passing through the points(-2,1) and (3,4)

2. Find the euation of line which makes an angle of 30 with x-axis and whose x- intercept is -2.

3. Find the equation of line which is parallel to the line and passing through the point (2,-3)

3.CIRCLE :-

1. Find the equation of the circle whose centre is (2,-3) and radious is 5 unit.

2. Find the centre and radious of the circle .

3. If the radious of a circle is is 4, find k.

4. Find the equation of tangent and normal to the circle at the point (3,4)

5.Find the equation of tangent and normal to the circle at the point (1,-2).

Assignment : - 3

FUNCTION & LIMIT

1. If , show that

2. If then prove that 3. If , then show that 4. Show that is an oddfuncion. 5. Find the range of te function if ,and domain is .

*Solve the following limits : -

1. 5.

2. 6.

3. 7.

4. 8.

9. 10.

Assignment: - 4

DIFFERENTIATION

1. Derivative using first principle: - 1. 2. 3. 4. 5. 6. Find the derivative of 7. If , find . 8. 2. Find . 1. 2. 3. . 4. 5.Find of for x = 1. 3. Differentiation of parametric functions: - 1. If and , then find 2. & 3. & 4. &

4. Differentiation of implicit functions: - 1. Find when .

2. If , prove that .

3. If , find

4. ,then show that

5. Derivative using logarithms: -(Find ) 1. , 2. 3.

6. Application:- 1. If the distance of a moving particle is given by . Find the velocity and at sec. 2. If the body moves such that , then find velocity when acceleration is zero. 3. The equation of of a particle , , (i) find the and acceleration at (ii) when do velocity and acceleration become equal? 4. Find the maximum and minimum for the function . 5. Find the maximum and minimum value of the function . 6. The motion of a particle is described by the equation . find velocity and acceleration at . 7. Find the maximum and minimum value of the function .

Assignment: - 5

INTEGRATION

1. If and , find . 2. Integrate .

3. Integrate .

4. Evaluate

5. Evaluate 6. Integrate of the following function. a. b. 7. Evaluate

8. Evaluate

9. Evaluate

10. Evaluate

11. Evaluate 12. Find the area under the line , bounded by and and - axis. 13. Find the area bounded by the curve , , and -axis and -axis. 14. Find the area of ellipse . 15. Find the area bounded by the curve , , . 16. Find the area bounded by the region enclosed by and .

Assignment: - 6

DIFFERENTIAL EQUATIONS

1. Formation of Differential Equations:- 1. Form a differential equation using 2. Find the differential equation for 3. The circle is given by . Form a differential equation. 2. Seperation of variables:- 1. Slov . 2. Slove . 3. Slov when , . 3. Homogeneous equations:- 1. Slove .

2. Slove .

3. Slove = 0. 4. Integrating Factor Method:- 1. Slove . 2. Slove . 3. Slove .

Assignment: -7

STATISTICS

1. Mean:- 1. The observations taken by the students in a laboratory using an electronic device are 22.7,22.3,22.4,21.08,22.0,23.01,22.7,22.4. Find the mean. 2. Mean of discrete observations:- 1. Find the mean observation for the following data: 42 40 35 38 41 43

9 8 3 5 10 7

3. Mean of grouped data:- 1. In a class of 60 students the height of the students in feet are described by the following table. Find the mean height: Height (feet) 4.0-4.5 4.5-5.0 5.0-5.5 5.5-6.0 No. of students 5 15 35 4

4. Step Deviation method:- 1. In a class of students the marks of a subject are given by the following table. Calculate the mean using Step Deviation Method. Marks 20-29 30-39 40-49 50-59 60-69 Students 05 11 18 22 14

5. Median:- 1. Find the median of the observations 6,9,3,4,8,7,10,12,11,13. 6. Median for grouped data :- 1. Find the median of the following grouped data. Class 0-5 5-10 10-15 15-20 20-25 25-30 Frequency 10 15 17 21 18 16

7. Mode:- 1. Find the mode of the following data. Marks 10- 20- 30- 40- 50- 60- 70- 80- 90- Below 20 30 40 50 60 70 80 90 100 Frequency 5 7 12 10 15 19 10 5 2

8. Standard Deviation:-

1. Find the S.D. of the data; 1,2,4,6,7,8,10,11.

9. S.D. for grouped data:- 1. Find the S.D. for the following table for the marks obtained in a branch of electronics . Marks 0-20 20-40 40-60 60-80 80-100 No.of 12 38 42 23 05 Students