BE Printing and Packaging Technology छमाही १ (इंजीनियरिंग) - University of Mumbai Important Questions

Using Principle of Virtual Work, determine the force P which will keep the weightless bar AB in equilibrium. Take length AB as 2m and length AC as 8m. The bar makes an angle of 30° with horizontal. All the surfaces in contact are smooth. Refer Figure 9.

Find the co-ordinate of the centroid of the area as shown in the given figure.

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

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.

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).

From (v-t) diagram find (1) Distance travelled in 10 second.
(2) Total distance travelled in 50 second.
(3) Retardation

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.

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

Determine the speed at which the basket ball at A must be thrown at an angle 30o so that if makes it to the basket at B.
Also find at what speed it passes through the hoop.

Figure shows a collar B which moves upwards with constant velocity of 1.5 m/s.At the instant when θ=50o.Determine :
(i)The angular velocity of rod pinned at B and freely resting at A against 25o sloping ground.
(ii)The velocity of end A of the rod.

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