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Engineering Mechanics : Question Paper May 2013 - First Year Engineering (Semester 1) | Mumbai University (MU)

## Engineering Mechanics - May 2013

### First Year Engineering (Semester 1)

TOTAL MARKS: 80

TOTAL TIME: 3 HOURS
(1) Question 1 is compulsory.

(2) Attempt any **three** from the remaining questions.

(3) Assume data if required.

(4) Figures to the right indicate full marks.
**1 (a)** Find forces P and Q such that resultant of given system is zero.

**1 (b)**A cylinder B, W

_{B}=1000 N, dia 40 cm, hangs by cable AB=40 cm rests against a smooth wall. Find out reaction at C and TAB. (4 marks)

**1 (c)**A block of weight 1000 N is kept on a rough inclined surface. Find out range of P for which the will block will be in equilibrium. (4 marks)

**1 (d)**A curvilinear motion of a particle is defined by V

_{X}= 25 - 8t m/s and y=48 - 3t

^{2}m. At t=0, x=0, Find out position, velocity and acceleration at t=4 sec.(4 marks)

**1 (e)**State D' Alembert's principle with two examples.(4 marks)

**2 (a)**Find out resultant of given (lever) forces system w.r.t. "B" (6 marks)

**2 (b)**Two identical cylinders dia 100 mm weight 200 N are placed as shown. All contacts are smooth. Find out reaction at A,B and C. (8 marks)

**2 (c)**A ball of mass m kg hits an inclined smooth surface with a velocity V

_{A}=3 m/s. Find out velocity of rebound. (6 marks)

**3 (a)**Find centoid of the shaded area. (8 marks)

**3 (b)**Explain conditions for equilibrium for forces in space.(6 marks)

**3 (c)**Explain work energy principle.(6 marks)

**4 (a)**Find the support reaction at Hinge A and Roller B. (8 marks)

**4 (b)**Explain x-t, v-t and a-t curves in Kinematics. (6 marks)

**4 (c)**Collar B moves up with velocity V

_{B}=2 m/s. Rod AB is pinned at B. Find out angular velocity of AB and velocity of A. (6 marks)

**5 (a)**Find out forces in FB and BE using method of section and other members by method of joints. (8 marks)

**5 (b)**A stone is thrown vertically upwards and returns to the starting point at the ground in 6 sec. Find out max. height and initial velocity of stone.(6 marks)

**5 (c)**Explain instantaneous centre of rotation.(6 marks)

**6 (a)**Force F=(3j - 4j + 12k)N acts at point A(1, -2, 3). Find -

(i) Moment of force about origin

(ii) Moment of forces about point B(2,1,2)m(4 marks)

**6 (b)**Find out min, value of P to start the motion. (8 marks)

**6 (c)**For a particle in rectilinear motion a= -0.05V

^{2}m/s

^{2}, at v=20 m/s, x=0. Find x at v=15 m/s and acc

_{n}at x=50 m.(4 marks)

**6 (d)**Sphere A is supported by two wires AB, AC. Find out tension in wire AC :-

(i) before AB is cut

(ii) just after AB is cut (4 marks)

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