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Sant Gadge Baba Amravati University (SGBAU)
B.E. First Year Engineering (Semester-I & II)
ENGINEERING MECHANICS
WINTER 2025 EXAMINATION
Time: Three Hours
Max. Marks: 80
SECTION - A
UNIT - 1
Q.1 (a) Define force. Explain the different systems of forces.
(4)
Q.1 (b) Determine magnitude and direction of resultant force for the system having following forces:
1. 20N force towards North-East
2. 10N force towards East
3. 50N force towards 30° West of North
4. 30N force towards South 40° West
1. 20N force towards North-East
2. 10N force towards East
3. 50N force towards 30° West of North
4. 30N force towards South 40° West
(6)
OR
Q.2 (a) Define equilibrium. State the different conditions of equilibrium.
(4)
Q.2 (b) A roller of radius 300mm and weighing 2000n is to be pulled over a curb of height 150mm as shown in figure by applying a horizontal force P applied to the end of a string wound around the circumference of the roller. Find the magnitude of force P required to start the roller mover over the curb.
(6)
UNIT - 2
Q.3 (a) Explain the various types of supports.
(3)
Q.3 (b) Find the support reactions for the given beam.
(7)
OR
Q.4 (a) State the assumptions use in analysis of truss.
(3)
Q.4 (b) Analyze the given frame as shown in figure.
(7)
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UNIT - 3
Q.5 (a) Define the terms: a) Angle of friction, b) Cone of friction.
(4)
Q.5 (b) Find the greatest value of W as shown in figure for the equilibrium of the system, if the coefficient of friction between body A and surface is 0.20 and between body B and surface is 0.28.
(6)
OR
Q.6 (a) Derive the angle of friction is always equals to angle of repose.
(3)
Q.6 (b) Determine the minimum force P required to move the wedge shown in figure. The angle of friction for all contact surfaces is 15°.
(7)
SECTION - B
UNIT - 4
Q.7 (a) State and explain parallel axis theorem.
(3)
Q.7 (b) Determine moment of inertia for section as shown in figure about centroidal yy axis.
(7)
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OR
Q.8 (a) Define the following terms: 1. Principal axes, 2. Principle moment of inertia.
(4)
Q.8 (b) Determine product of inertia of shaded area about given X and Y - axis.
(6)
UNIT - 5
Q.9 (a) The rectilinear motion of a particle is defined by a = 12t - 6t². It starts from rest when t = 0. Determine its velocity when it returns to its initial position.
(5)
Q.9 (b) Car A had a start with an acceleration of 2 m/s². Car B comes 5 sec after car A to chase car A with a uniform velocity of 20 m/s. find the time taken by car B to catch car A.
(5)
OR
Q.10 (a) A particle moves in x-y plane and its position is given by, r̄ = (3t)i + (4t - 3t²)j. Find radius of curvature of its path and total acceleration when it crosses x-axis again.
(7)
UNIT - 6
Q.11 (a) State and explain D'Alembert principle.
(3)
Q.11 (b) Determine the velocity of body A after it has moved 6m starting from rest. Use D'Alembert principle.
(7)
OR
Q.12 (a) Derive Work-Energy equation for translation.
(8)
Q.12 (b) After the block shown in figure has moved 4m starting from rest the constant force P is removed. Find the velocity of block when it returns to its initial position. The coefficient of friction μ = 0.2. Use work-Energy equation.
(6)
IMPORTANT FORMULA SHEET
Momentum: M = Force × Distance
Lami's Theorem: P/sinα = Q/sinβ = R/sinγ
Friction: F = μN
Work-Energy: ΣW = ½mv₂² - ½mv₁²
Parallel Axis: I = Ig + Ah²
D'Alembert: ΣF - ma = 0
Student Notes:
1. Always start with a Free Body Diagram (FBD) for every numerical.
2. For Unit 1, resolve forces into horizontal (ΣFx) and vertical (ΣFy) components.
3. Unit 4 requires careful integration or part-summation of sections.
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