**Engineering Mechanics Question paper May 2013** – The engineering mechanics E.M question paper for mumbai university students of semester 2 who are in F.E first year is given below:

### Engineering Mechanics Question paper May 2013

1 (a) Find forces P and Q such that resultant of given system is zero.

4 M

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 M

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 M

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 M

1 (e) State D’ Alembert’s principle with two examples.

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2 (a) Find out resultant of given (lever) forces system w.r.t. “B”

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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.

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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 M

3 (a) Find centoid of the shaded area.

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

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3 (c) Explain work energy principle.

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

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

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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 M

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

8 M

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.

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5 (c) Explain instantaneous centre of rotation.

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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

(i) Moment of force about origin

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

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

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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 M

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

(i) before AB is cut

(ii) just after AB is cut

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