University Question with Answer

University Question with Answer

Q.1

A ball is projected with an initial velocity of u at an angle of a with the horizontal.

Derive the expresions for x and y positions of the ball in terms of time t. Also derive the expressions for the time of flight, maximum height attained and horizontal range.

Ans. : 

Refer section 9.7.

May-2017

Engineering Mechanics

Semester - II (Mechanical / Civil) Regulation 2013

[Time: Three Hours] [Maximum Marks: 100]

Answer ALL Questions

AU Solved Paper (71945)

PART A - (10 × 2 = 20 Marks)

Q.1

State the principle of transmissibility. 

[Refer Two Marks Q.9 of chapter - 1] 

Q.2

Find the resultant and direction of force

[Refer Two Marks Q.24 of chapter - 1]

Q.3

Differentiate between moment and couple. 

[Refer Two Marks Q.5 of chapter - 3]

Q.4

A uniform ladder of weight 'W' leans against a vertical wall. Assuming the contact surfaces as rough, draw the free body diagram of the ladder with necessary assumptions. 

[Refer Two Marks Q.12 of chapter - 8]

Q.5

Differentiate between center of gravity and centroid.

[Refer Two Marks Q.1 of chapter - 5]

Q.6

State parallel axis theorem as applied to area moment of inertia.

[Refer Two Marks Q.3 of chapter - 6]

Q.7

The displacement of a particle is given by S = 3t2+2t meters, where 't' is in seconds. Find the velocity and acceleration when t = 10 seconds. 

[Refer example 9.1.1]

Q.8

State the principle of work-energy. 

[Refer Two Marks Q.10 of chapter - 9]

Q.9

What is dry friction? 

[Refer Two Marks Q.10 of chapter - 8]

Q.10

What is general plane motion? Given one example. 

[Not in New Syllabus] 

PART B - (5 × 16 = 80 Marks)

Q.11

a) Two cylinders E, F of diameter 60 mm and 30 mm. Weighing 160 N and 40 N respectively are placed as shown in Fig. 1. Assuming all the contact surfaces to be smooth, find the reactions at A, B and C. 

[Refer example 2.11.22]

b) Forces 32 kN, 24 kN, 24 kN and 120 kŃ are concurrent at origin (0, 0, 0) and are respectively directed through the points whose coordinates are A(2, 1, 6),

B(4, -2, 5), C(-3, -2, 1) and D(5, 1, − 2). Determine resultant of the system. 

[Refer example 2.12.15]

Q.12 

a) Four tug boats are used to bring a large ship to its pier. Each tug boat exerts a 5000 N force in the direction as shown in Fig. 2. Determine the equivalent force-couple system at point 'O' and the point on hull where a single more-powerful tugboat should push to produce the same effect as the original four tugboats. 

[Refer example 3.7.11]

b) A light bar AD is suspended from a cable BE and supports a 50 kg block at C as shown in Fig. 3. The ends A and D of the bar in contact with frictionless vertical walls. Determine the tension in cable BE and the reactions at A and D. 

[Refer example 4.6.36]

Q.13 

a) Determine the .location of centroid for the right angle triangle from the first principles and find the volume of cone using Pappus-Guldinus theorem.

[Refer examples 5.2.2 and 5.4.1]

OR

b) Calculate the moment of inertia of the section shown in Fig. 4 about "x" and "y" axes through the centroid. 

[Refer similar example 6.6.7]

Q.14 

a) A body moving with uniform acceleration is observed to travel 33 m in 8th second and 53 m in 13th second of its travel. Calculate the velocity at start and uniform acceleration. 

[Refer example 9.1.38]

OR

b) Two blocks 'A' and 'B' of masses mA = 280 kg and m B = 420 kg are joined by an inextensible cable as shown in Fig. 5. Assume that the pulley is frictionless and μ = 0.30 between block 'A' and the surface. The system is initially at rest. Determine 

i) Acceleration of block A;

ii) Velocity after it has moved 3.5 m and

iii) Velocity after 1.5 seconds. 

[Refer example 9.2.23]

Q.15

a) A 100 N force acts on a 300 N block placed on an inclined plane as shown in Fig. 6. The coefficient of friction between the block and the plane are μs = 0.25 and μh = 0.20. Determine whether the block is in equilibrium and find the value of the friction force. 

[Refer example 8.6.9]

OR

b) A wheel is attached to the shaft of an electric motor of rated speed of 2000 rpm. When the power is switched on, the wheel attains the rated speed in 10 seconds and when the power is switched off, the unit comes to rest in 100 seconds. Assume uniformly accelerated motion and determine the number of revolutions the unit turns (i) To attain the rated speed and (ii) To come to rest. 

[Not in New Syllabus]