Answer any one question from Q1 & Q2

1 (a)
Find the magnitude of the resultant and its location of the following forces acting at a point O as shown in Fig. 1.a

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1 (b)
A Particle starts with an initial velocity of 2.5 m/s and uniformly accelerates at the rate 0.5 m/s

^{2}. Determine the displacement in 2 s, time required to attain the velocity of 7.5 m/s and the distance travelled when it attain a velocity of 7.5 m/s.
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2 (a)
Determine the position of centroid of the shaded area as shown in Fig. 2a with respect to origin O.

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2 (b)
Two weights 100 N and 30 N are connected by a string and move along a rough horizontal plane under the action of force 50 N applied to the first weight 100 N as shown in Fig. 2 b. The coefficient of friction between the sliding surfaces of the weights and plane is 0.25. Determine the acceleration of weights and the tension in the string using Newton's second law.

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Answer any one question from Q3 & Q4

3 (a)
A square foundation supports four loads as shown in Fig. 3 a. Determine magnitude, direction and point of application of resultant of four forces.

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3 (b)
Two sphere P and Q each of weight 50 N and a radius of 100 mm rest in horizontal channel of width 360 mm as shown in Fig. 3 b. Determine the reaction at the point of contact A, B and C.

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3 (c)
A particle is projected at an angle of 30° to the horizontal with a velocity of 100 m/s. Determine the range of radius of curvature of the path followed by the particle.

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4 (a)
Three loads are applied as shown in Fig. 4 a. to a light beam supported by cables attached at B and C. Neglecting the weight of the beam, determine the range of values of Q for which neither cable becomes slack when P = 0.

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4 (b)
A 200 kg cylinder is hung by means of two cables AB and AC, which isattached to the top of vertical wall. A horizontal force P perpendicular to thewall holds the cylinder in the position shown in Fig. 4 b. Determine the magnitudeof P and the tension in each cable

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4 (c)
A 150 kg car enters a curved portion of the road of radius 200 m travelling at a constant speed of 36 km/h. Determine the normal and tangential component of force at curved portion.

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Answer any one question from Q5 & Q6

5 (a)
A plane truss is loaded and supported as shown in Fig.5 a. Determine the magnitude and nature of forces in all the members.

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5 (b)
A body of weight 300 N is kept on a rough horizontal plane and a force P is applied to just move the body horizontally as shown in Fig. 5 b. Find the magnitude of force P required if coefficient of static friction is ?

_{s}=0.4.

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5 (c)
A car of mass 1500 kg is moving down a hill having a slope of 15° to the horizontal. At the time, when the car is moving at a speed of 10 m/s, the driver applies the brakes. Calculate the average force applied parallel to the hill slope that will stop the car in a distance of 30 m. Use work energy principle.

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6 (a)
Determine the reactions at A, D and tension in BC of the rope ABCD loaded and supported as shown in Fig.6 a.

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6 (b)
A 100 N ladder AB of length 6 m rest against a vertical wall and horizontal floor as shown in Fig. 6 b. Determine the slope of the ladder with vertical to maintain equilibrium if the coefficient of static friction at all contact surface is ?

_{s}=0.25.

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6 (c)
Determine the velocities of the two balls shown in Fig. 6 C after impact. Take weight of ball A is 20 N, weight of ball B is 10 N and coefficient of restitution is 0.6

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