Que. No  Question Statement  Que. No  Question Statement 
Centroid and C.G.  
1  Determine the Y coordinate of Centroid of the shaded area as shown in Figure. (May 13)
Ans: = 0 mm, = 8.36 mm
 2  Determine the Y coordinate of Centroid of the shaded area as shown in Figure. (Dec 13)
Ans: = 100 mm, = 79.96 mm

3  A thin rod is bent into a shape OABCD as shown in Figure. Determine the Centroid of the bent rod with respect to origin O. (May 14) Ans: = 116.67 mm, = 25 mm
 4  Determine the coordinate of Centroid of the shaded area as shown in Fig. (Dec 14) Ans: = 300 mm, = 225 mm 
5  Determine the X & Y coordinates of the Centroid with respect to the origin O of the shaded area as shown in Fig. (May 15) Ans: = 243.63 mm, =  6  A semicircular area is cut from a trapezium as shown in Fig. Determine the Centroid of the shaded portion with respect to the origin. (Dec 15) Ans: = 150 mm, = 90.84 mm

7  A slender rod is welded into the shape as shown in Fig. Locate the position of Centroid of the rod with respect to origin O if AO=BO=CO=50 mm. (May 16) Ans: = 00 mm, = mm
 8  Determine the Y coordinate of Centroid of the shaded area as shown in Figure. (Dec 16)
Ans: = 100 mm, = 69.9 mm

9  Determine the position of centroid of the shaded area with respect to origin O as shown in Fig. (May 17) Ans: = 86.67 mm, = 86.67 mm  10  Locate the centroid of the shaded area obtained by cutting a semicircle of diameter ‘a’ from the quadrant of a circle of radius ‘a’ as shown in Fig. with respect to origin O. (Dec 17)
Ans: = 0.358 a, = 0.64 a

11  Locate the centroid of the plane lamina as shown in figure. (May 18)
Ans: = =
 12  Locate the centroid of the plane lamina as shown in figure. (Dec 18) Ans: = 46.19 = 47.83

13  Locate the centroid of the shaded area as shown in figure. Ans: = 3.72 cm = 3.72 cm
 14  Locate the centroid of the shaded area as shown in figure. Ans: = 107.41 mm = 107.41 mm

15  Find the value of distance ‘a’ So that centroid of the uniform lamina shown in Fig. remains at the centre of rectangle ABCD. (Dec2002) Ans: a = 21.58 cm
 16  Locate the centroid of the shaded area as shown in figure with respect to given axes. Ans: = 28.48 mm, = 38.18 mm 
Moment of Inertia  
1  Determine the M.I. of the ‘I’ section about x and y axis passing through its C.G. as shown in figure.  2  Determine the M.I. of the Composite section about x and y axis passing through its C.G. as shown in figure. 
3  Determine the M.I. of the ‘I’ section about its Centroidal xx and yy axis. The particulars are: Top Flange  300 mm x 20 mm Web 20m x 300 mm Bottom flange 150 mm x20 mm  4  Determine the M.I. of the ‘I’ section about xx and yy axis as shown in figure. The particulars are: Top Flange  300 mm x 20 mm Web 20m x 300 mm Bottom flange 150 mm x20 mm 
5  Determine the MI of the shaded area as shown in Figure about X axis passing through its bottom edge.
 6  Determine the MI of the shaded area as shown in Figure about Centroid X and Y axis.

Friction  
1  A uniform hoop of weight W is suspended from the peg at A and a horizontal force P is slowly applied at B as shown in fig. if the hoop begins to slip at A when θ = 30°. Determine the coefficient of static friction between the hoop and the peg.  2  The uniform pole of length l and mass m is leaned against the vertical wall as shown in Fig. If the coefficient of static friction between supporting surfaces and the ends of the pole is 0.25, calculate the maximum angle θ at which the pole may place before it starts to slip. 
3  The 15 m ladder has a uniform weight of 80 N and rest against the smooth wall at B as shown in Fig. If the coefficient of static friction μs= 0.4, determine if the ladder will slip?  4  The 15 m ladder has a uniform weight of 80 N. It rests against smooth vertical wall at B and horizontal floor at A. If the coefficient of static friction between ladder and floor at A is μs = 0.4, determine the smallest angle θ with vertical wall at which the ladder will slip. 
5  Determine the distance ‘s’ to which the 90 kg man can climb without causing the 4 m ladder to slip at its lower end. The top of the 15 kg ladder has a small roller and at the ground the coefficient of static friction is µs = 0.25. The mass centre of the man is directly above his feet.  6  The uniform rod having a weight W and length L is suppported at its ends A and B as shown in Fig. where the coefficient of static friction μs = 0.2. Determine the greatest angle θ so that the rod does not slip. Refer Fig. 
7  The homogeneous semicylinder has a mass m and mass centre at G as shown in Fig. Determine the largest angle θ of the inclined plane upon which it rest so that it does not slip down the plane. The coefficient of static friction between the plane and cylinder is 0.3.  8  A block of mass m rest on a frictional plane which makes an angle α with the horizontal as shown in Fig. If the coefficient of friction between the block and the frictional plane is 0.2, determine the angle α for limiting condition. 
9  Determine the range of P for the limiting equilibrium of block B of mass 150 kg rest on an inclined plane as shown in Fig.
μs = 0.3  10  A 400 N block is resting on a rough horizontal surface as shown in Fig. for which the coefficient of friction is 0.4. Determine the force P required to cause motion if applied to the block horizontally. What minimum force is required to start motion? 
11  Determine the horizontal force P needed to just moving the 300 N block up the plane. Take μs= 0.3 and refer Fig.  12  Determine the horizontal force P needed to just start moving the 30 kg block up the plane as shown in fig. Take μs = 0.25 and μk = 0.25 
13  A block of mass 10 kg rests on an inclined plane as shown in Fig. If the coefficient of static friction between the block and plane is μs = 0.25, determine the maximum force P to maintain equilibrium.  14  Determine the horizontal force P needed to just start moving the 300 N crate up the plane as shown in Fig. Take µs = 0.1. 
15  Determine the range of cylinder weight W as shown in Fig. 6 b for which the system is in equilibrium. The coefficient of friction between cord and cylindrical support surface is 0.3 and that between100 N block and the incline surface is zero.  16  Determine the range of P for the equilibrium of block of weight W as shown in Fig. The coefficient of friction between rope and pulley is 0.2. 
17  A cable is passing over the disc of belt friction apparatus at a lap angle 180° as shown in Fig. If the weight of block is 500 N, Determine the range of force P to mainntain equilibrium.  18  A chain having a weight of 1 .5 N/m and total length of 10 m is suspended over a peg P as shown in Fig. If the coefficient of static friction hetwen the peg and cord is μs = 0.25, determine the largest length h which one side of the suspended cord can have without causing motion. Neglect the size of peg. 
19  Determine the minimum coefficient of static friction between the rope and the fixed shaft as shown in Fig. 6 will prevent the unbalanced cylinder from moving.  20  A force P = mg/6 is required to lower the cylinder with the cord making 1.25 turns around t.he fixed shaft. Determine the coefficient of friction between the cord and the shaft. Refer Fig. 
21  The spool has a mass of 200 kg and rest against the wall and on the beam shown in Fig. If the coefficient of static friction at B is μB = 0.3 and the wall is smooth, determine the friction force developed at B when the vertical force applied to the cable is P = 800 N.  22 
