AMIETE – ET (OLD SCHEME)

Code: AE03 Subject: APPLIED MECHANICS

Time: 3 Hours Max. Marks: 100

NOTE: There are 9 Questions in all.

· Question 1 is compulsory and carries 20 marks. Answer to Q.1 must be written in the space provided for it in the answer book supplied and nowhere else.

· Out of the remaining EIGHT Questions answer any FIVE Questions. Each question carries 16 marks.

· Any required data not explicitly given, may be suitably assumed and stated.

Q.1 Choose the correct or the best alternative in the following: (2 10)

a. If flow conditions satisfy ‘Laplace equation’ then

(A) flow is rotational

(B) flow does not satisfy continuity equation

(C) flow is irrotational and satisfy continuity equation

(D) flow is irrotational and does not satisfy continuity equation

b. A simply supported beam of span ‘l’ carries two point loads of each of magnitude ‘w’ acing ‘l/4’ from both the ends, the shear force at the center of the beam will be

(A) w/4 (B) w/2

(C) w (D) Zero

c. Maximum value of frictional force acting on a body, when the body is just about to start is called

(A) limiting friction (B) static friction

(C) dynamic friction (D) none

d. The ratio of maximum horizontal shear stress to the mean stress in a circular beam is

(A) 2/3 (B) 3/2

(C) 3/4 (D) 4/3

e. While analyzing a truss, it has been assumed that the external loads act only at

(A) joints (B) members

(C) supports (D) none

f. Newton-meter is the unit of

(A) force (B) momentum

(C) moment (D) deflection

g. A screw is self locking if the friction angle is________helix angle

(A) less than (B) more than

(C) equal to (D) none

h. For analyzing a frame by method of joints, a joint is selected where number of unknowns are not more than:

(A) 2 (B) 3

(C) 4 (D) 5

i. The C.G. of a triangular lamina lies at a point where the three medians of the triangle meet

(A) True (B) False

j. In a velocity-time graph, the area under the curve is

(A) distance travelled by the particle

(B) change in acceleration

(C) change in velocity

(D) time taken to attain the velocity

Answer any FIVE Questions out of EIGHT Questions.

Each question carries 16 marks.

Q.2 a. Define collinear force and non- concurrent force. (4)

b. An iron ball is attached to rope of 0.5 meter long at one of its ends. The other end of the rope is attached to the hook on the roof such that the iron ball is suspended vertically. The ball weighs 50 N. If this ball is to be held 10 cm above the lowest position. Determine the magnitude and direction of the least force. Also find the tension in the rope at that point. (12)

Q.3 a. Prove that the expression for centroid of a semicircular lamina of radius ‘r’ is given by (4r/3 π). (8)

b. Find the centroid of the shaded area shown in Fig.1. (8)

Fig. 1

Q.4 a. Define

(i) perfect frame (ii) deficient frame (iii) redundant frame (3)

b. A two-dimensional truss is loaded as shown in Fig.2. Determine the forces in each member of the truss using method of joints and tabulate the results. (13)

.

Fig.2

Q.5 a. Derive equation for the work done by force of gravity. (6)

b. The equation of motion of a particle moving in a straight line is given by x = 15t + 3t² – t³

where x is in meters and t is in seconds. Find

(i) the velocity and acceleration at start

(ii) the time when the particle reaches its maximum velocity

and the corresponding position

(iii) the maximum velocity of the particle (10)

Q.6 a. The block shown in Fig.3 has a mass of 6 kg. It is attached to a cord which is wrapped around the periphery of a 20 kg disk that has a moment of inertia I_A = 0.40 kg-m². If the block is initially moving downward with a speed of 2 m/sec, determine its speed in 3 secs. Neglect the mass of the cord. (8)

Fig.3

b. Determine the angular velocities of link AB and BD shown in Fig.4. (8)

Fig.4

Q.7 A beam has been subjected to force and moment as shown in Fig.5 Determine shear force and bending moment and draw S.F.D. and B.M.D. Mark the values of the important ordinates. (16)

Fig.5

Q.8 a. A shaft of 0.2 m diameter and 300 cm length is subjected to torque of N-m. Find the relative rotation between the end cross section of the shaft. Take N/mm². (8)

b. A wooden tie is 60 mm wide, 120 mm deep and 1.5 m long. It is subjected to an axial pull of 30 kN. The stretch of the member is found to be 0.625 mm. Determine Young’s modulus of the tie material. (8)

Q.9 a. Briefly discuss “Dimensional Homogeneity”. (6)

b. The diameter of a water pipe is suddenly enlarged from 350 mm to 700 mm. The rate of flow through it is 0.25 m³/s and the pressure in the smaller pipe is 7.5 N/m². Calculate

(i) the loss of head in the enlargement

(ii) the power lost due to enlargement and

(iii) the pressure in the larger pipe if the pipe line is horizontal. (10)