Date: December 2016

(1)Question no.**1** is **compulsory.**

(2) Attempt any 3 questions from remaining five questions.

Find the force F^{4} , so as to give the resultant of the force as shown in the figure given below.

Given : Forces and their resultant

To find : Force F^{4}

Chapter: [1] System of Coplanar Forces

A particle starts from rest from origin and it’s acceleration is given by a = `k/(x+4)^2 m⁄s^2`.Knowing that v = 4 m/s when x = 8m,find :

(1)Value of k

(2)Position when v = 4.5 m/s

Given : Particle starts from rest

a = `k/(x+4)^2 m⁄s^2`

v = 4m/s at x = 8m

To find : Value of k and position when v= 4.5m/s

Chapter: [11.01] Force and Acceleration

Rod AB of length 3 m is kept on a smooth plane as shown in the given figure.The velocity of end A is 5 m/s along the inclined plane.Locate the ICR and find velocity of end B.

Given : Length of rod AB = 3m

va = 5 m/s**To find**: ICR

Velocity of end B

Chapter: [10] Kinematics of Rigid Bodies

What is a zero force member in a truss? With examples state the conditions for a zero force member.

Chapter: [5] Analysis of Plane Trusses

A glass ball is dropped on a smooth horizontal floor from which it bounces to a height of 9m.On the second bounce it rises to a height of 6 m.From what height was the ball dropped and find the coefficient of restitution between the glass and the floor.

**Given** : First bounce height = 9 m

Second bounce height = 6 m**To find** : Co-efficient of restitution

Chapter: [9] Kinematics of Particle

The given figure shows a beam AB hinged at A and roller supported at B. The L shaped portion is welded at D to the beam AB. For the loading shown,find the support reactions.

**Given** : Beam AB hinged at A and roller supported at B and different forces acting on it.**To find :** Support reactions

Chapter: [4] Types of Support

The acceleration time diagram for a linear motion is shown. Construct velocity time diagram and displacement time diagram for the motion assuming that the motion starts with a initial velocity of 5 m/s from the starting point.

**Given** : Acceleration time graph**To draw** : Velocity time graph

Displacement time graph

Chapter: [9] Kinematics of Particle

The resultant of the three concurrent space forces at A is š¯‘¹Ģ… = (-788š¯’‹Ģ…) N. Find the magnitude of F1,F2 and F3 forces.

**Given** : A=(0,12,0)

B=(-9,0,0)

C=(0,0,5)

D=(3,0,-4)

Resultant of forces = (-788š¯‘—Ģ…) N**To find** : Magnitude of forces F1,F2,F3

Chapter: [1] System of Coplanar Forces

Two spheres A and B of weight 1000N and 750N respectively are kept as shown in the figure..Determine reaction at all contact points 1,2,3 and 4. Radius of A is 400 mm and radius of B is 300 mm

**Given ** : Two spheres are in equilibrium

W_{1}=1000 N

W_{2}=750 N

r_{A}=400 mm

r_{B}=300 mm **To find : Reaction forces at contact points 1,2,3 and 4**

Chapter: [3] Equilibrium of System of Coplanar Forces

A circle of diameter 1.5 m is cut from a composite plate.Determine the centroid of the remaining area of plate.

Chapter: [9] Kinematics of Particle

A rod AB has an angular velocity of 2 rad/sec,counter clock wise as shown.End C of rod BC is free to move on a horizontal surface.Determine:

(1)Angular velocity of rod BC

(2)Velocity of C

**Given** : ωAB=2 rad/sec (anti clockwise)

**To find** : ωBC

VC

Chapter: [9] Kinematics of Particle

A truss is loaded and supported as shown.Determine the following:

(1)Identify the zero force members,if any

(2)Find the forces in members EF,ED and FC by method of joints.

(3)Find the forces in members GF,GC and BC by method of sections

Chapter: [5] Analysis of Plane Trusses

b)A cylinder has a mass of 20kg and is released from rest when h=0 as shown in the figure.Determine its speed when h=3m.The springs have an unstretched length of 2 m.Take k=40 N/m.

**Given** : m=20 kg

h=0

k=40 N/m**To find **: Speed when h=3m

Chapter: [11.02] Work and Energy

A machine part is subjected to forces as shown.Find the resultant of forces in magnitude and in direction.

Also locate the point where resultant cuts the centre line of bar AB.

**Solution**:**Given** : A machine subjected to various forces**To find** : Resultant of forces

Point where the resultant force cuts the bar AB

Chapter: [1] System of Coplanar Forces

Two blocks A and B are resting against the wall and floor as shown in the figure.Find the minimum value of P that will hold the system in equilibrium. Take μ=0.25 at the floor,μ=0.3 at the wall and μ=0.2 between the blocks.

**Given** : μ=0.25 at floor

μ=0.2 between blocks**To find** : Minimum value of force P

Chapter: [3] Equilibrium of System of Coplanar Forces

A shot is fired with a bullet with an initial velocity of 20 m/s from a point 10 m infront of a vertical wall 5 m high.

Find the angle of projection with the horizontal to enable the shot to just clear the wall. Also find the range of the shot where the bullet falls on the ground.

**Given** : u=20 m/s

Distance from wall=10m

Height of wall=5m**To find** :Angle of projection

Range of shot

Chapter: [9] Kinematics of Particle

Three blocks A,B and C of masses 3 kg,2 kg and 7 kg respectively are connected as shown.Determine the acceleration of A,B and C.Also find the tension in the string.

Given : m_{A}=3kg

m_{B}=2 kg

m_{C}=7kg **To find: **Acceleration of blocks A,B and C

Chapter: [3] Equilibrium of System of Coplanar Forces

Block A of weight 2000N is kept on the inclined plane at 35° .It is connected to weight B by an inextensible string passing over smooth pulley.

Determine the weight of pan B so that B just moves down.Assume μ=0.2.

**Given** : Weight of block A=2000N

Angle of inclined plane = 35°

μ=0.2**To find** : Weight of pan B

Chapter: [3] Equilibrium of System of Coplanar Forces

A particle falling under gravity travels 25 m in a particular second. Find the distance travelled by it in the next 3 seconds.

**Given** : Particle falls 25 m in a particular second

Sn=-25 m

u=0 m/s**To find** : Distance travelled by it in next 3 seconds

Chapter: [9] Kinematics of Particle

A rod AD of length 40 cm is suspended from point D as shown in figure. If it has a weight of 25 N and also supports a load of 40N,find the tension in the cable using the method of virtual work.Take AC=30 cm.

**Given** : Length of rod AD=40cm=0.4m

AC=0.3m

W=25N

Load on rod AD=40N**To find** : Tension in the cable

Chapter: [3] Equilibrium of System of Coplanar Forces

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