BE Automobile Engineering सत्र १ (इंजीनियरिंग) - University of Mumbai Question Bank Solutions

The V-X graph of a rectilinear moving particle is shown. Find the acceleration of the particle at 20m,80 m and 200 m

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.

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 

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

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

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).

State Lami’s theorem.
State the necessary condition for application of Lami’s theorem.

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