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

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.

A 75kg person stands on a weighing scale in an elevator. 3 seconds after the motion starts from rest, the tension in the hoisting cable was found to be 8300N. Find the reading of the scale, in kg during this interval. Also find the velocity of the elevator at the end of this interval. The total mass of the elevator, including mass of the person and the weighing scale, is 750kg. If the elevator is now moving in the opposite direction, with same magnitude of acceleration, what will be the new reading of the scale?

Find the weight WB so as to have its impending motion down the plane. Take weight of block A as 2kN. The pin connected rod AB is initially is in horizontal position. Refer Figure 13. Coefficient of friction = 0.25 for all surfaces.

Two springs, each having stiffness of 0.6N/cm and length 20 cm are connected to a ball B of weight 50N. The initial tension developed in each spring is 1.6N. The arrangement is initially horizontal, as shown in Figure 14. If the ball is allowed to fall from rest, what will be its velocity at D, after it has fallen through a height of 15 cm?

Two balls, A (mass 3kg) and B (mass 4kg), are moving with velocities 25 m/s and 40 m/s respectively (Refer Figure 15). Before impact, the direction of velocity of two balls are 300 and 500 with the line joining their centers as shown in Figure 15. If coefficient of restitution for the impact is 0.78, find the magnitude and the direction of velocities of the balls after the impact.

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

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.

Compute the resultant of three forces acting on the plate shown in the figure. Locate it’s intersection with AB and BC.

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

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
W₁=1000 N
W₂=750 N
r_A=400 mm
r_B=300 mm 
To find : Reaction forces at contact points 1,2,3 and 4

If the support reaction at A, for the beam shown in Figure 3, is zero, then find force ‘P’ and the support reaction at B. 

From the top of a tower, 28 m high, a stone is thrown vertically up with a velocity of 9m/s. After how much time will the stone reach the ground? With what velocity does it strike the ground?

The cylinder B, diameter 400mm and weight 5kN, is held in position as shown in Figure 12 with the help of cable AB. Find the tension in the cable and the reaction developed at contact C.

A force of 140 kN passes through point C (-6,2,2) and goes to point B (6,6,8). Calculate moment of force about origin.