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Applied Mechanics and Graphic Statics

Applied Mechanics and Graphic Statics
A particle moves in a straight line and its position is defined by the equation x = 6 t² - t3 where t is expressed in seconds and ‘x’ in meters. The maximum velocity during the motion is

48 m/sec
24 m/sec
6 m/sec
12 m/sec

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Applied Mechanics and Graphic Statics
The ratio of the ranges on the inclined plane with motion upward and with motion downward for a given velocity, angle of projection will be

sin (α - β)/sin (α + β)
cos (α - β)/cos (α + β)
sin (α + β)/sin (α - β)
tan (α - β)/tan (α + β)

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Applied Mechanics and Graphic Statics
Which of the following represents the state of neutral equilibrium?

None of these
A smooth cylinder lying on a convex surface
A smooth cylinder lying on a curved surface
A cube resting on one edge

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Applied Mechanics and Graphic Statics
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

100 kg
40 kg
60 kg
10 kg

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Applied Mechanics and Graphic Statics
If the given forces P₁, P₂, P₃ and P₄ are such that the force polygon does not close, then the system will

Always reduce to a resultant force
Be in equilibrium
Always reduce to a couple
Both (A) and (C)

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Applied Mechanics and Graphic Statics
The ends of a string weighing w/metre are attached to two points at the same horizontal level. If the central dip is very small, the horizontal tension of the string throughout is

wl²/16d
wl²/4d
wl²/8d
wl/4d

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