BE Mechanical Engineering Semester 1 (FE First Year) - University of Mumbai Question Bank Solutions for Engineering Mechanics

A homogeneous cylinder 3 m diameter and weighing 400 N is resting on two rough inclined surface’s shown.If the angle of friction is 15o.Find couple C applied to the cylinder that will start it rotating clockwise.

Blocks P₁ and P₂ are connected by inextensible string.Find velocity of block P₁,if it falls by 0.6 m starting from rest.
The co-efficient of friction is 0.2.The pulley is frictionless.

Co-ordinate distance are in m units for the space frame in figure.
There are 3 members AB,AC and AD.There is a force W=10 kN acting at A in a vertically upward direction.
Determine the tension in AB,AC and AD.

Just before they collide,two disk on a horizontal surface have velocities shown In figure.
Knowing that 90 N disk A rebounds to the left with a velocity of 1.8 m/s.Determine the rebound velocity of the 135 N disk B.Assume the impact is perfectly elastic.

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

The acceleration of the train starting from rest at any instant is given by the expression `a=8/(v^2+1)` where v is the velocity of train in m/s. Find the velocity of the train when its displacement is 20 m and its displacement when velocity is 64.8 kmph.

A boom AB is supported as shown in the figure by a cable runs from C over a small smooth pulley at D.
Compute the tension T in cable and reaction at A.Neglect the weight of the boom and size of the pulley.

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

Angular velocity of connector BC is 4 r/s in clockwise direction.What is the angular velocities of cranks AB and CD?

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

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

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

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

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 

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

Find the resultant of the parallel force system shown in Figure 1 and locate the same with respect to point C. 

Using Instantaneous Centre of Rotation (ICR) method, find the velocity of point A for the instant shown in Figure 2. Collar B moves along the vertical rod, whereas link AB moves along the plane which is inclined at 25⁰. Ɵ = 45⁰

The link CD of the mechanism shown in Figure 7 is rotating in counterclockwise direction at an angular velocity of 5 rad/s. For the given instance, determine the angular velocity of link AB.

Cylinder A (diameter 1m, weight 20 kN) and cylinder B (diameter 1.5m, weight 40 kN) are arranged as shown in Figure 8. Find the reactions at all contact points. All contacts are smooth. 

Velocity-time diagram for a particle travelling along a straight line is shown in Figure 10. Draw acceleration-time and displacement-time diagram for the particle. Also find important values of acceleration and displacement.