BE Mechanical Engineering सत्र १ (इंजीनियरिंग) - University of Mumbai Question Bank Solutions for Engineering Mechanics

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.

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

Find the force ‘F’ to have motion of block A impeding up the plane. Take coefficient of friction for all the surfaces in contact as 0.2. Consider the wedge B as weightless. Refer Figure 11.

A particle moves in x-y plane with acceleration components a_x = -3m/s² and ay = -16t m/s². If its initial velocity is V₀ = 50m/s directed at 35⁰ to the x–axis, compute the radius of curvature of the path at t = 2 sec.

A force of magnitude of 20kN, acts at point A(3,4,5)m and has its line of action passing through B(5,-3,4)m. Calculate the moment of this force about a line passing through points S(2,-5,3) m and T(-3,4,6)m.

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

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.