Solve any one question from Q1 and Q2

1 (a)
The force system shown in Fig. 1(a) have a resultant of 200 N along positive Y-axis, determine the magnitude and position θ of force F.

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1 (b)
Two blocks are connected by an inextensible string as shown in Fig. 1(b). If the system is released from rest, determine the velocity of the block A after it has moved 2 m by work energy principle. The coefficient of friction between block A and the plane is μ

_{S}=0.25.

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1 (c)
A stone is dropped from the top of a tower 50 m high. At the same time, another stone is thrown vertically upwards from the foot of tower with a velocity of 25 m/s. When and where the two stones cross each other?

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1 (d)
A cricket ball thrown by a fielder from a height of 2m at an angle of 45° to the horizontal with an initial velocity of 25 m/s hit the wicket at the height of 0.6m from the ground, find distance of fielder from the wickets:

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2 (a)
A semicircular area is cut from a trapezium as shown in Fig. 2(a). Determine the centroid of the shaded portion with respect to the origin.

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2 (b)
A pendulum bob has a mass of 10 kg and is released from rest when θ=0° as shown in Fig. 2(b). Determine the tension in the cord at θ=30°. Neglect the size of bob.

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2 (c)
A ball is dropped from an unknown height on a horizontal floor from which it rebounds to height of 8 m. If e=0.667, calculate the height from which the ball was dropped.

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2 (d)
A bullet moving at a speed of 300 m/s has its speed reduce to 270 m/s when it passes through a board. Determine how many such boards the bullet will penetrate before it stops.

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Solve any one question from Q3 and Q4

3 (a)
A simply supported beam AB of span 6m is loaded and supported as shown in Fig. 3(a). Find the reactions at supported A and B.

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3 (b)
Determine the magnitude and direction of a resultant force of a given force system as shown in Fig. 3(b) and locate its point of application on the slab:

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3 (c)
A sphere weighing 1000 N is placed in a wrench as shown in Fig. 3(c), find the reactions at the point of contacts:

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4 (a)
Determine the magnitude and position of force F so that the force system shown in Fig. 4(a) maintain equilibrium.

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4 (b)
If each cable can sustain a maximum tension of 600 N, determine the greatest weight of the bucket and its contents that can be supported. Refer Fig. 4(b).

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4 (c)
Determine the reactions at roller A and pin B for equilibrium of the member ACB as shown in Fig. 4(c).

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Solve any one question from Q5 and Q6

5 (a)
Members AB and BC can support a maximum compressive force of 800 N and members AD, DC and BD can support a maximum tensile force of 2000 N. Determine the greatest load P the truss can support. Refer Fig. 5(a).

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5 (b)
The uniform rod having a weight W and length L is supported at its ends A and B as shown in Fig. 5(b), where the coefficient of static friction μ

_{s}=0.2. Determine the greatest angle θ so that the rod does not slip. Refer Fig. 5(c)

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5 (c)
Determine the horizontal force P needed to just start moving the 300 N crate up the plane. Take μ

_{s}=0.3. Refer Fig. 5(c).

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6 (a)
Determine the force in the member BE and BD of the truss which supports the load as shown in Fig. 6(a). All interior angles are 60° and 120°.

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6 (b)
Determine the magnitude of pin reactions at A, B and D for the frame loaded as shown in Fig. 6(b).

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6 (c)
A force P=mg/6 is required to lower the cylinder with the cord making 1.25 turns around the fixed shaft. Determine the coefficient of friction μ

_{s}between the cord and the shaft. Refer Fig. 6(c):

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