Stresses of Hollow Circular Tube Used as a Pole

Situation
A 12-m pole is fixed at its base and is subjected to uniform lateral load of 600 N/m. The pole is made-up of hollow steel tube 273 mm in outside diameter and 9 mm thick.
1.   Calculate the maximum shear stress (MPa).

A.   0.96 C.   1.39
B.   1.93 D.   0.69

2.   Calculate the maximum tensile stress (MPa).

A.   96.0 C.   60.9
B.   69.0 D.   90.6

3.   Calculate the force (kN) required at the free end to restrain the displacement.

A.   2.7 C.   27
B.   7.2 D.   72

 

Centripetal Force of a Ball Revolving Uniformly in a Horizontal Circle

Problem
A 150 g ball at the end of a string is revolving uniformly in a horizontal circle of radius 0.600 m. The ball makes 2 revolutions in a second. What is the centripetal acceleration?

A.   74.95 m/sec2 C.   49.57 m/sec2
B.   94.75 m/sec2 D.   59.47 m/sec2

 

Sum of Areas of Infinite Number of Squares

Problem
The side of a square is 10 m. A second square is formed by joining, in the proper order, the midpoints of the sides of the first square. A third square is formed by joining the midpoints of the second square, and so on. Find the sum of the areas of all the squares if the process will continue indefinitely.
 

Radius of Circle of New Atom Smasher

Problem
A new kind of atom smasher is to be composed of two tangents and a circular arc which is concave toward the point of intersection of the two tangents. Each tangent and the arc of the circle is 1 mile long, what is the radius of the circle? Use 1 mile = 5280 ft.

A.   1437 ft. C.   1347 ft.
B.   1734 ft. D.   1374 ft.

 

Sum of Areas of Equilateral Triangles Inscribed in Circles

Problem
An equilateral triangle is inscribed within a circle whose diameter is 12 cm. In this triangle a circle is inscribed; and in this circle, another equilateral triangle is inscribed; and so on indefinitely. Find the sum of the areas of all the triangles.
 

Ratio of Volume of Water to Volume of Conical Tank

Problem
A conical tank in upright position (vertex uppermost) stored water of depth 2/3 that of the depth of the tank. Calculate the ratio of the volume of water to that of the tank.

A.   4/5 C.   26/27
B.   18/19 D.   2/3

 

Finding The Length Of Parabolic Curve Given Change In Grade Per Station

Problem
A +0.8% grade meets a -0.4% grade at km 12 + 850 with elevation 35 m. The maximum allowable change in grade per station is 0.2%. Determine the length of the curve.

A.   300 m C.   80 m
B.   240 m D.   120 m

 

Find y’ if x = 2 arccos 2t and y = 4 arcsin 2t

Problem
Find y’ if x = 2 arccos 2t and y = 4 arcsin 2t.

A.   2 C.   4
B.   -2 D.   -4

 

Probability That A Randomly Selected Chord Exceeds The Length Of The Radius Of Circle

Situation
If a chord is selected at random on a fixed circle what is the probability that its length exceeds the radius of the circle?

  1. Assume that the distance of the chord from the center of the circle is uniformly distributed.
    A.   0.5 C.   0.866
    B.   0.667 D.   0.75
  2. Assume that the midpoint of the chord is evenly distributed over the circle.
    A.   0.5 C.   0.866
    B.   0.667 D.   0.75
  3. Assume that the end points of the chord are uniformly distributed over the circumference of the circle.
    A.   0.5 C.   0.866
    B.   0.667 D.   0.75

 

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