MOI (SEM. II) EXAMINATION.

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Problems Based On Centroid And MOI (SEM. II) EXAMINATION. 2006-07 1- Find the centroid of a uniform wire bent in form of a quadrant of the arc of a circle of radius R.

4- Find the second moment of area of the given L-section about the centroidal x axis as shown in Fig.5 (SEM.

1 Problems Based On Centroid And MOI (SEM. II) EXAMINATION Find the centroid of a uniform wire bent in form of a quadrant of the arc of a circle of radius R. 2- State the parallel axis theorem. 3- What is product of inertia? What will the product of inertia of a circular disc about its centroidal axis? 4- Find the second moment of area of the given L-section about the centroidal x axis as shown in Fig.5 (SEM. II) EXAMINATION, (AG ) 5- Determine the moment of inertia about xx - axis and yy-axis for the unequal angle section 200 x 100 x 10 mm. (SEM. I) EXAMINATION A triangle is removed from a semicircle as shown in figure. Locate the centroid of the remaining object. 7- Derive an expression for the centroid of semicircular arc. 8- Explain any three of the following (i) Second moment of area. (ii) Radius of Gyration (iii) Parallel axis theorem (iv) Perpendicular axis theorem. 9- Derive an expression for mass moment of inertia of solid sphere about axis passing through its center ODD SEMESTER THEORY EXAMINATION For the Z-section as shown in Fig. 3, the moment of inertia with respect to x and y axes are given. Determine the principal axes of the section about O (centroid of vertical section and point O coincides) and values of the principal moments of inertia Copyright by Brij 2013 Page 1

11- A semicircular area is removed from the trapezoid as shown in Fig. 7. Determine the centroid of remaining area.

13- Derive an expression of mass moment of inertia of a circular lamina about the central axis.

of inertia 15- Determine the moment of inertia of T section about the horizontal and vertical axes, passing through the

17- Determine the mass moment of inertia of a rectangular plate of size a x b and thickness t about the centroidal axis.

2 11- A semicircular area is removed from the trapezoid as shown in Fig. 7. Determine the centroid of remaining area. 12- Explain the following : ( i ) Product of inertia (ii) Principal moment of inertia. 13- Derive an expression of mass moment of inertia of a circular lamina about the central axis. (SEM II) EVEN SEMESTER THEORY EXAMINATION, Explain the following: (i) Product of inertia (ii) Mass moment of inertia 15- Determine the moment of inertia of T section about the horizontal and vertical axes, passing through the CG. of the section as shown Figure Locate the centroid of channel section as shown in Figure Determine the mass moment of inertia of a rectangular plate of size a x b and thickness t about the centroidal axis. (SEM. I) ODD SEMESTER THEORY EXAMINATION Find the principal moment of inertia about the origin of the area shown in figure. All dimensions are in mm. Copyright by Brij 2013 Page 2

19- A wire is bent into a closed loop A-B-C-D-E-A as shown in figure in which portion AB is circular arc.

20- Derive an expression for moment of inertia of a solid sphere about its diameter.

If the system is released from horizontal position in rest condition, find the magnitude of angular acceleration.

(SECOND SEMESTER)THEORY EXAMINATION, 2010-11 22- A semicircular area is removed from the trapezoid as shown in Fig.

23- Calculate the moment of inertia of the composite area shown in Fig. 3 about the centroidal axis.

3 19- A wire is bent into a closed loop A-B-C-D-E-A as shown in figure in which portion AB is circular arc. Determine the centroid of the wire. 20- Derive an expression for moment of inertia of a solid sphere about its diameter. 21- A homogeneous sphere weighing 10 kg is attached to a slender rod of mass 2 kg. If the system is released from horizontal position in rest condition, find the magnitude of angular acceleration. Also find angular velocity of system when it passes through vertical position. (SECOND SEMESTER)THEORY EXAMINATION, A semicircular area is removed from the trapezoid as shown in Fig.. 8. Determine the centroid of the remaining area. 23- Calculate the moment of inertia of the composite area shown in Fig. 3 about the centroidal axis. 24- Stale and prove the theorems of parallel and perpendicular axis with suitable example. 25- Derive an expression for the mass moment of inertia of a circular disc of radius R and thickness t about its centroidal axis. (SEM. II) THEORY EXAMINATION Determine the area moment of inertia of an ellipse about its centroidal axes. Copyright by Brij 2013 Page 3

27- Determine the centroid and moment of inertia of the area shown about centroidal x-axis.

longitudinal axis. 29- Determine the centroid of a thin wire bent in shape of W as shown in figure.

31- Define centre of gravity and centroid.

33- Derive an expression for the mass moment of inertia of a right circular cone about its axis.

4 27- Determine the centroid and moment of inertia of the area shown about centroidal x-axis. 28- Determine the mass moment of inertia of a solid cylinder of radius R and height h about its longitudinal axis. 29- Determine the centroid of a thin wire bent in shape of W as shown in figure. (SEMESTER-I) THEORY EXAMINATION, State the theorem of perpendicular axis. 31- Define centre of gravity and centroid. 32- State and prove the theorems of parallel and perpendicular axis. 33- Derive an expression for the mass moment of inertia of a right circular cone about its axis. 34- Calculate the moment of inertia of the hatched section shown in Fig. 3 about the centroidal X-X axis. 35- Determine the moment of inertia of T section about the horizontal and vertical axes, passing through the C.G. of the section as shown in Fig. 7. (SEM. II) THEORY EXAMINATION Determine length of wire such that centroid is located at point 'O'. Find the length in terms of 'r' Fig. 9. Copyright by Brij 2013 Page 4

37- Determine the moment of Inertia of the shaded area with respect to x and y axis. Fig.

39- What is the moment of Inertia of a square plate of side 'a' about its diagonal?

41- Explain the product of Inertia and principal moment of Inertia.

Determine the acceleration with which the assembly will rotate about point 'A', if released from rest in horizontal position.

43- A motor provides a constant torque of M = 150 Nm to a hoisting pulley of mass 25 kg and mass moment of Inertia 0.9 kg m 2.

(SEMESTER-II) THEORY EXAMINATION, 2011-12 44- Define product moment of Inertia and polar moment of Inertia.

5 37- Determine the moment of Inertia of the shaded area with respect to x and y axis. Fig Product of inertia of an area about an axis is zero. Explain. 39- What is the moment of Inertia of a square plate of side 'a' about its diagonal? 40- Determine mass moment of inertia of a solid cylinder of radius R and height h about its centroidal axis. 41- Explain the product of Inertia and principal moment of Inertia. 42- A cylinder weighing 500 N is welded to a 1 m long uniform bar of 200 N as shown in Fig. 3. Determine the acceleration with which the assembly will rotate about point 'A', if released from rest in horizontal position. Determine the reaction at 'A' at this instant. 43- A motor provides a constant torque of M = 150 Nm to a hoisting pulley of mass 25 kg and mass moment of Inertia 0.9 kg m 2. The pulley lifts 200 N block starting from rest. Determine speed of block after it rises by 2 m. Fig. 12. (SEMESTER-II) THEORY EXAMINATION, Define product moment of Inertia and polar moment of Inertia. 45- Differentiate between centroid and center of gravity. 46- Determine the moment of Inertia of the built -up section shown in Fig. 3 about its centroidal axis x-x and y-y. 47- A cylinder weighing 500 N is welded to a 1.0 m long uniform bar of 200 N as shown in Fig. 8. Determine the acceleration with which the assembly will rotate about point A, if released from rest in horizontal position determine the section at A at this instant. 48- Write short note on Principal moment of Inertia and Mass moment of Inertia. 49- Determine the centroid of a sector of a circle of radius R and central angle 2a. 50- Determine the moment of Inertia of a solid sphere of radius R about its diametral axis. Copyright by Brij 2013 Page 5

(SECOND SEMESTER) CARRY OVER THEORY EXAMINATION 2011-12 51- Differentiate between centre of

53- Calculate the moment of inertia of T section about an axis parallel to the base of the T

G of a channel section 100 x 50 x 15 mm as shown in figure.

56- Find the moment of inertia of the section shown in figure about centroidal horizontal

CARRY OVER EXAMINATION, 2011-12 57- Differentiate between centroid and centre of gravity.

58- Calculate the second moment of the shaded area shown in Fig.

6 (SECOND SEMESTER) CARRY OVER THEORY EXAMINATION Differentiate between centre of gravity and centroid. 52- Define radius of gyration. 53- Calculate the moment of inertia of T section about an axis parallel to the base of the T and passing through its centre of gravity. 54- Find the C. G of a channel section 100 x 50 x 15 mm as shown in figure. 55- What are perpendicular and parallel axis theorems? Discuss their application. 56- Find the moment of inertia of the section shown in figure about centroidal horizontal axis. SPL. CARRY OVER EXAMINATION, Differentiate between centroid and centre of gravity. Under what conditions do they coincide? 58- Calculate the second moment of the shaded area shown in Fig.3 about the horizontal centroidal axis. 59- Determine the product of inertia of a right angled triangle (fig.7) with respect to the centroidal axes parallel to x and y axes. 60- Derive the expression for the mass moment of inertia of a cylinder of length /, radius r and density p about the horizontal centroidal axis parallel in the base. Copyright by Brij 2013 Page 6

61- For a z-section shown in Fig. 8, the moments of inertia with respect to x and y are given to be I x = 1548 cm 4 and I y = 2668 cm 4.

I) ODD SEMESTER THEORY EXAMINATION 2012-13 62- Determine the principal moment of inertia of the area shown in Fig. 2 for axes through origin.

64- Compute the mass moment of inertia of right circular cone of radius r and height h about an axis passing through apex and normal to its base.

(SEMESTER II) EVEN SEMESTER THEORY EXAMINATION, 2012-13 66- Define centre of gravity and centroid. 67- State parallel axis theorem.

70- Calculate the mass moment of inertia of the body shown in Fig. 10, with respect to vertical geometrical axis.

7 61- For a z-section shown in Fig. 8, the moments of inertia with respect to x and y are given to be I x = 1548 cm 4 and I y = 2668 cm 4. Determine the principal axes of the section about O and the values of the principal moment of inertia. (SEM. I) ODD SEMESTER THEORY EXAMINATION Determine the principal moment of inertia of the area shown in Fig. 2 for axes through origin. 63- Find the centroid of the area under half sine curve shown in Fig. 11. Find the centroid of this area about axis A A'. 64- Compute the mass moment of inertia of right circular cone of radius r and height h about an axis passing through apex and normal to its base. 65- A uniform rod of length 20 cm is bent at an angle of 90 from the middle. Find the distance of C.G. of the rod from its middle point about which the rod is bent. (SEMESTER II) EVEN SEMESTER THEORY EXAMINATION, Define centre of gravity and centroid. 67- State parallel axis theorem. 68- Locate the centroid of the lamina shown in Fig Find the moment of inertia of I-section shown in Fig. 9, about its centroidal axes. 70- Calculate the mass moment of inertia of the body shown in Fig. 10, with respect to vertical geometrical axis. Assume density of cone and cylinder are 6500 Kg/m 3 and 7850 kg/m 3 respectively. (SEMESTER-I) THEORY EXAMINATION, Give centroid of quarter circle arc. 72- Define radius of gyration with respect to x-axis of an area. 73- Determine the centroid of semicircular area of radius r using method of integration. 74- Explain: (i) Parallel axes theorem (ii) Perpendicular axes theorem 75- Find the moment of area of the diagram shown in Fig. 4, about its centroidal axes. Copyright by Brij 2013 Page 7

(SEM. II) EVEN THEORY EXAMINATION 2012-13 76- A circular arc of radius 1 m has a central angle of

77- Distinguish between the moment of inertia of an area and its polar moment of inertia.

79- Locate the centroid of area under curve x = ky 3 from x = 0 to x = a.

81- Determine the mass moment of inertia of a right circular cone about its longitudinal axis. (SEM.

with figure. 83- For the shaded area shown in figure-3.

84- Find the centroid of the shaded area with respect to x and y axis by direct integration method.

8 (SEM. II) EVEN THEORY EXAMINATION A circular arc of radius 1 m has a central angle of 45. Locate its centroid. 77- Distinguish between the moment of inertia of an area and its polar moment of inertia. 78- Calculate the polar moment of inertia of the shaded area about point O. 79- Locate the centroid of area under curve x = ky 3 from x = 0 to x = a. 80- Determine the area moment of inertia for the given triangular area about x axis. 81- Determine the mass moment of inertia of a right circular cone about its longitudinal axis. (SEM. I) ODD SEMESTER THEORY EXAMINATION Write down the statement of parallel axis theorem with figure. 83- For the shaded area shown in figure-3. find the moment of inertia about the line AB. 84- Find the centroid of the shaded area with respect to x and y axis by direct integration method. (Ref. figure-8) 85- Find the mass M.I. (Moment of inertia) of a rectangular plate of mass m, base b and height h about the centroidal axis parallel to the base. (SEM. II) EXAMINATION Find the moment of inertia of plane lamina about x-axis and also find its radius or gyration k x (Figure--3): Copyright by Brij 2013 Page 8

87- Find the centroid of a wire bent in a shape ABCDA as shown in Figure-10.

of a right circular cone of base radius 'R' and mass 'M' about its symmetrical axis (SEM.

90- Explain difference between centroid and center of gravity.

92- Calculate the moment of inertia of section about the centroidal axis. (Fig.

as shown in Fig 3 about the XX and YY centroidal axes All dimensions are in mm 95- Calculate the

9 87- Find the centroid of a wire bent in a shape ABCDA as shown in Figure Derive an expression for M.I. of a right circular cone of base radius 'R' and mass 'M' about its symmetrical axis (SEM. I / I I) SPECIAL CARRY OVER THEORY EXAMINATION, State the Parallel axis theorem. 90- Explain difference between centroid and center of gravity. 91- Prove that centre of gravity of hemisphere lies at 3r/8 from the base. 92- Calculate the moment of inertia of section about the centroidal axis. (Fig. 8) 93- Determine the mass moment of inertia of a cone of radius R about the centroidal axis. (SEM. I) (ODD SEM.) THEORY EXAMINATION, Determine the moment of inertia of beam's cross sectional area as shown in Fig 3 about the XX and YY centroidal axes All dimensions are in mm 95- Calculate the mass moment of inertia of the cylinder of radius 0 5 m, height 1 m and density 2400 kg/m 3 about the centroidal axis (Fig 4) 96- Find the centroid of an L-section of 120 mm X 80 mm X 20 mm. (SEM. I) (COP) (ODD SEM.) THEORY EXAMINATION, Determine the centroid of a uniform lamina as shown in figure-1. Copyright by Brij 2013 Page 9

10 98- Determine the M.I. of the shaded area as shown in figure-7 about the centroidal axis X-X. 99- Determine the mass moment of inertia of a solid right circular cone of base radius 'R' and height 'h' about its axis of rotation. Copyright by Brij 2013 Page 10

Sub:Strength of Material (22306)

Sub:Strength of Material (22306) UNIT 1. Moment of Inertia 1.1 Concept of Moment of Inertia (Ml). Effect of MI in case of beam and column. 1.2 MI about axes passing through centroid. Parallel and Perpendicular