# Engineering Mechanics CBCGS 2017-2018 BE Mechanical Engineering Semester 1 (FE First Year) Question Paper Solution

Engineering Mechanics [CBCGS]
Date: December 2017

 1 | Attempt any four questions
 1.a

state and prove varigon’s theorem.

Concept: Varignon’s Theorem
Chapter:  System of Coplanar Forces
 1.b

Find the resultant of the force system as shown in the given figure. Concept: Resultant of concurrent forces
Chapter:  System of Coplanar Forces
 1.c

Find the co-ordinate of the centroid of the area as shown in the given figure. Concept: Velocity and Acceleration in Terms of Rectangular Co-ordinate System
Chapter:  Kinematics of Particle
 1.d

A force of 500 N is acting on a block of 50 kg mass resting on a horizontal surface as shown in the figure. Determine the velocity after the block has travelled a distance of 10m. Co efficient of kinetic friction is 0.5. Concept: Cone of Friction
Chapter:  Friction
 1.e

The position vector of a particle which moves in the X-Y plane is given by 𝒓̅ = (3t3-4t2)𝒊̅ + (0.5t4)𝒋̅

Concept: Velocity and Acceleration in Terms of Rectangular Co-ordinate System
Chapter:  Kinematics of Particle
 2
 2.a

Find the resultant of the force acting on the bell crank lever shown. Also locate its position with respect to hinge B. Given : Forces on the bell crank lever
To find : Resultant and it’s position w.r.t hinge B

Concept: Resultant of parallel forces
Chapter:  System of Coplanar Forces
 2.b

Determine the reaction at points of constant 1,2 and 3. Assume smooth surfaces. Given: The spheres are in equilibrium
To find: Reactions at points 1,2 and 3 Concept: Condition of Equilibrium for non-concurrent nonparallel general forces
Chapter:  Equilibrium of System of Coplanar Forces
 2.c

Two balls having 20kg and 30 kg masses are moving towards each other with velocities of 10 m/s and 5 m/s respectively as shown in the figure.
If after the impact ,the ball having 30 kg mass is moving with 6 m/s velocity to the right then determine the coefficient of restitution between the two balls. Concept: Velocity and Acceleration in Terms of Rectangular Co-ordinate System
Chapter:  Kinematics of Particle
 3
 3.a

Determine the position of the centroid of the plane lamina. Shaded portion is removed. Concept: Centroid for Plane Laminas
Chapter:  Center of Gravity and Centroid for Plane Laminas
 3.b

Explain the conditions for equilibrium of forces in space.

Concept: Condition of equilibrium for concurrent forces
Chapter:  Equilibrium of System of Coplanar Forces
 3.c

A 30 kg block is released from rest.If it slides down from a rough incline which is having co-efficient of friction 0.25.Determine the maximum compression of the spring.Take k=1000 N/m. Concept: Equilibrium of Bodies on Inclined Plane
Chapter:  Friction
 4
 4.a

Find the support reactions at A and B for the beam loaded as shown in the given figure. Concept: Condition of equilibrium for parallel forces
Chapter:  Equilibrium of System of Coplanar Forces
 4.b

The V-X graph of a rectilinear moving particle is shown. Find the acceleration of the particle at 20m,80 m and 200 m Concept: Velocity and Acceleration in Terms of Rectangular Co-ordinate System
Chapter:  Kinematics of Particle
 4.c

A bar 2 m long slides down the plane as shown.The end A slides on the horizontal floor with a velocity of 3 m/s.Determine the angular velocity of rod AB and the velocity of end B for the position shown. Concept: Velocity and Acceleration in Terms of Rectangular Co-ordinate System
Chapter:  Kinematics of Particle
 5
 5.a

Referring to the truss shown in the figure. Find :
(a) Reaction at D and C
(b)Zero force members.
(c)Forces in member FE and DC by method of section.
(d)Forces in other members by method of joints. Concept: Analysis of Plane Trusses by Using Method of Joints
Chapter:  Analysis of Plane Trusses
 5.b

Determine the force P required to move the block A of 5000 N weight up the inclined plane, coefficient of friction between all contact surfaces is 0.25. Neglect the weight of the wedge and the wedge angle is 15 degrees. Given : Weight of block A = 5000 N
μs=0.25
Wedge angle = 15º

To find : Force P required to move block A up the inclined plane Concept: Condition of equilibrium for concurrent forces
Chapter:  Equilibrium of System of Coplanar Forces
 5.c

Determine the tension in a cable BC shown in fig by virtual work method. Given: F=3500 N
ϴ = 50o
Length of rod = 3.75 mm + 1.5 mm = 5.25 mm
To find : Tension in cable BC

Concept: Applications on Equilibrium Mechanisms
Chapter:  Principle of Virtual Work
 6
 6.a

A 500 N Crate kept on the top of a 15° sloping surface is pushed down the plane with an initial velocity of 20m/s. If μs = 0.5 and μk = 0.4, determine the distance travelled by the block and the time it will take as it comes to rest. Given: Weight of crate = 500 N

Initial velocity(u) = 20 m/s

μs = 0.5

μk = 0.4

θ = 15°

Final velocity (v) = 0 m/s
To find: Distance travelled by the block Time it will take before coming to rest

Concept: Velocity and Acceleration in Terms of Rectangular Co-ordinate System
Chapter:  Kinematics of Particle
 6.b

Derive the equation of path of a projectile and hence show that equation of path of projectile is a parabolic curve.

Concept: Velocity and Acceleration in Terms of Rectangular Co-ordinate System
Chapter:  Kinematics of Particle
 6.c

particle is moving in X-Y plane and it’s position is defined bybar r=(3/2 t^2)bar l+(2/3 t^3) barJ "Find radius of curvature when t=2sec."

Concept: Velocity and Acceleration in Terms of Rectangular Co-ordinate System
Chapter:  Kinematics of Particle
 6.d

A Force of 100 N acts at a point P(-2,3,5)m has its line of action passing through Q(10,3,4)m. Calculate moment of this force about origin (0,0,0).

Concept: Velocity and Acceleration in Terms of Rectangular Co-ordinate System
Chapter:  Kinematics of Particle

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