Applied Mechanics and Graphic Statics

81. A stone of mass 1 kg is tied to a string of length 1 m and whirled in a horizontal circle at a constant angular speed 5 rad/sec. The tension in the string is,

1. 5 N
2. 10 N
3. 15 N
4. 25 N

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82. A stone was thrown vertically upwards from the ground with a velocity of 50 m/sec. After 5 seconds another stone was thrown vertically upwards from the same place. If both the stones strike the ground at the same time, then the velocity with which the second stone was thrown should be (Assume g = 10 m/sec²)

1. 15 m/sec
2. 25 m/sec
3. 40 m/sec
4. 50 m/sec

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83. A string of length 90 cm is fastened to two points and at the same level 60 cm apart. A ring weighing 120 g is slided on the string. A horizontal force is applied to the ring such that it is in equilibrium vertically below . The value of is:

1. 40 g
2. 60 g
3. 80 g
4. 100 g

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84. A system of coplanar forces acting on a rigid body can be reduced to

1. One force only
2. One couple only
3. One force and one couple only
4. None of the above

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85. A system of coplanar forces is in equilibrium when

1. Force polygon closes
2. Funicular polygon closes
3. Both force polygon and funicular polygon close
4. All the forces are concurrent

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86. A train weighing 196 tonnes experiences a frictional resistance of 5 11/22 per tonne. The speed of the train at the top of a down gradient 1 in 78.4 is 36 km/hour. The speed of the train after running 1 km down the slope, is

1. 5√10 m/sec
2. 10√5 m/sec
3. 5√3 m/sec
4. 3√5 m/sec

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87. A trolley wire weighs 1 kg per metre length. The ends of the wire are attached to two poles 20 m apart. If the horizontal tension is 1000 kg, the central dip of the cable is

1. 2 cm
2. 3 cm
3. 4 cm
4. 5 cm

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88. A uniform pyramid and a uniform prism of same height lie with their base on the surface. Which is more stable?

1. Pyramid
2. Prism
3. Both equally stable
4. None of the above

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89. A uniform rod 9 m long weighing 40 kg is pivoted at a point 2 m from one end where a weight of 120 kg is suspended. The required force acting at the end in a direction perpendicular to rod to keep it equilibrium, at an inclination 60° with horizontal, is

1. 40 kg
2. 60 kg
3. 10 kg
4. 100 kg

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90. A vehicle weighing 'w' kg is to run on a circular curve of radius 'r' . If the height of its centre of gravity above the road level is 'h' and the distance between the centres of wheels is 2a, the maximum velocity, in order to avoid over turning, will be

1. gra/h
2. √(gra/h)
3. ∛ (gra/h)
4. ∜ (gra/h)

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