Question Paper: Engineering Mechanics Question Paper - Dec 17 - First Year Engineering (Semester 1) - Mumbai University (MU)
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Engineering Mechanics - Dec 17

First Year Engineering (Semester 1)

Total marks: 80
Total time: 3 Hours
INSTRUCTIONS
(1) Question 1 is compulsory.
(2) Attempt any three from the remaining questions.
(3) Draw neat diagrams wherever necessary.
(4) Take $g=9.81m/s^2$

Q1) Attempt any four:

1(a) State and prove varignones theorem.
(5 marks) 00

1(b) Find the resultant of the force system shown in fig.

<em>figure</em>

(5 marks) 00

1(c) Find the co-ordinate of the centroid of the area shown in fig.

<em>figure</em>

(5 marks) 2910

1(d) A force of 500N is acting on a black of 50Kg mass resting on a horizontal surface as shown in fig. Determine the velocity after the block has traveled a distance of 10m. Coeff. of kinetic friction = 0.5.

<em>figure</em>

(5 marks) 3051

1(e) The position vector of a particle which moves in the X-Y plane is given by $\bar r = (3t^3 - 4t^2)i + (0.5t^4)J m.$ Calculate velocity and acceleration at t=1 sec.
(5 marks) 00

2(a) Find the resultant of the force acting on the bell crank level shown. Also locate its position write hinge B.

<em>figure</em>

(8 marks) 2585

2(b) Determine the reaction at points of constant 1,2 and 3. Assume smooth surfaces.

<em>figure</em>

(6 marks) 00

2(c) Two balls having 20Kg and 30Kg masses are moving towards each other with velocities of 10m/s and 5m/s respectively as shown in fig. If other impact the ball having 30Kg mass is moving with 6m/s velocity to the right then determine the coefficient of restitution between the two balls.
(6 marks) 00

3(a) Determine the centroid of the plant lamina shaded portion is removed.

<em>figure</em>

(8 marks) 2917

3(b) Explain conditions for equilibrium for forces in spaces.
(6 marks) 00

3(c) A 30N block is released from rest. If slides down a rough incline having coefficient of friction 0.25. Determine the maximum compression of the spring.

<em>figure</em>

(6 marks) 00

4(a) Find the support reaction at A and B for the beam loaded as shown in fig.

<em>figure</em>

(8 marks) 2953

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

<em>figure</em>

(6 marks) 3015

4(c) A bar AB 2m long slides down the plane as shown. The end A slides on the horizontal floor with a velocity of 3m/s. Determine the angular velocity of the rod AB and the velocity of end B for the position shown.

<em>figure</em>

(6 marks) 00

5(a) Referring to the truss shown in fig. Find

  • i) Reaction at D and C
  • ii) Zero Force members
  • iii) Forces in members FE and DC by method of section.
  • iv) Forces in other members by method of joints.

<em>figure</em>

(8 marks) 2951

5(b) Determine the force 10 required to move the block A of 5000N weight up the inclined plane, coefficient of friction between all contact surfaces is 0.25. Neglect the weight of the wedge and the wedge angle is 15 degrees.

<em>figure</em>

(6 marks) 2974

5(c) Determine the tension in a cable BC shown in fig by virtual work method.

<em>figure</em>

(6 marks) 00

6(a) A 500N crate kept on the top of a $15^0$ sloping surface is pushed down the plane with an initial velocity of 20m/s. If $\mu s = 0.5$ and $\mu k = 0.4$. Determine the distance travelled by the block and the time it will take as it comes to rest.
(5 marks) 00

6(b) Derive the equation of the path of a prosotile and hence show that the path traced by a prosectile is a parabolic curve.
(5 marks) 00

6(c) A particle is moving in X-Y plane and its position is defined by $\bar r = (\frac{3}{2}t^2) i + ( \frac{2}{3}t^3)J.$

Find ratio of curvature when t = 2 sec.

(5 marks) 00

6(d) A force of 100N 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).
(5 marks) 2971

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