Solve any one question from Q.1(a,b,c,d) & Q.2(a,b,c,d)

1(a)
The resultant of two forces P and Q is 1400 N vertical. Determine the force Q and the corresponding angle θ for the system of forcess as shown in Fig. 1A.

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1(b)
The system shown in Fig. 1b is initially at rest. Neglecting axle friction and mass of pulley, determine the acceleration of block.

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1(c)
A cricket ball shot by a batsman from a height of 2.0 m at an angle of 30° with the horiziontal with a velocity of 20 m/s is caught by a fielder at a height of 0.8 m from the ground. Determine the distance between the batsman and fielder.

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1(d)
A ball has a mass of 30 kg and is thrown upward with a speed of 15 m/s. Determine the time to attain maximum height using impulse momentum principle. Also find the maximum height.

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2(a)
Determine the y coordinate of centroid of the shaded area as shown in Fig. 2a.

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2(b)
If the crest of the hill has a radius of curvature ρ = 60m, determine the maximum constant speed at which the car can travel over it without leaving the surface of the road. The car has a weight of 17.5kN. (Refer Fig. 2b)

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2(c)
A particle moves along a straight line with an acceleration α=(4t

^{3}- 2t), where α is in m/s^{2}and t is in s. When t = 0, the practicle is at 2 m to the left of origin and when t = 2s the praticle is at 20 m to left of origin. Determine the position of particle at t = 4s.
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2(d)
A woman having a mass of 70 kg stands in an elevator which has a downward acceleration of 4 m/s

^{2}starting from rest. Determine work done by her weight and the work of the normal force which the floor exerts on her when the elevator descends 6 m.
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Solve any one question from Q.3(a,b,c) & Q.4(a,b,c)

3(a)
Two spheres A and B a diameter 80 mm and 120 mm respectively are held in equilibrium by separate strings as shown in Fig. 3a. Sphere B rests against vertical wall. If masses of spheres A and B are 10 kg and 20 kg, determine the tension in the string and reactions at point of contact.

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3(b)
Four parallel bolting forces act on the rim of the circular cover plate as shown in Fig. 3b. If the resultant force 750 N is passing through (0.15m, 0.1m) from the origin O, determine the magnitude of force P

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_{1}and P_{2}!mage

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3(c)
Determine the support reaction for the beam loaded and supported as shown in Fig. 3c. !mage

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4(a)
Three cables are joined at the junction C as shown in Fig. 4a. Determine the tension in cable AC and BC caused by the weight of the 30 kg cylinder.

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4(b)
The square steel plate has a mass of 1800 kg with mass center G as shown in Fig. 4b. Determine the tension in each cable so that the plate remains horiziontal.

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4(c)
Determine the component of reaction at hinge A and tension in the cable BC as shown in Fig. 4c.

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Solve any one question from Q.5(a,b,c) & Q.6(a,b,c)

5(a)
A block of mass 10 kg rests on an inclined plane as shown in Fig. 5a. If the coefficient of static friction between the block and plane is μ

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_{s}= 0.25, determine the maximum force P to maintain equalibrium.!mage

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5(b)
Determine the components of reactions at supports A and B for the frame loaded and supported as shown in Fig. 5b.

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5(c)
The 15 m ladder has uniform weight of 80N. It rests against smooth vertical wall at B and horiziontal floor at A. If the coefficient of static friction between ladder and floor at A is μ

_{s}=0.4, determine the smallest angle θ with vertical wall at which the ladder will slip.
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6(a)
The cable segment support the loading as shown in Fig. 6a. Determine the support reaction and maximum tension in segment of cable.

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6(b)
A cable is passing over the disc of belt friction apparatus at a lap angle 180° as shown in Fig. 6b. If the weight of block is 500 N, determine the range of force P to maintain equilibrium.

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6(c)
Determine the forces in the members of the truss loaded and supported as shown in the Fig. 6c. Tabulate the result with magnitude and nature of force in the members.

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