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The polar moment of inertia of a hollow circular shaft of outer diameter (D) and inner diameter (d) is

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WBPSC JE Civil 2018 Official Paper
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  1. \(\frac{\pi}{16}\times (D^3-d^3)\)
  2. \(\frac{\pi}{16}\times (D^4-d^4)\)
  3. \(\frac{\pi}{32}\times (D^4-d^4)\)
  4. \(\frac{\pi}{64}\times (D^4-d^4)\)

Answer (Detailed Solution Below)

Option 3 : \(\frac{\pi}{32}\times (D^4-d^4)\)
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Detailed Solution

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Explanation:

Polar moment of inertia of Solid cylinder:

\({I_Z} = J = \frac{{\pi {D^4}}}{{32}}\)

Polar moment of inertia of Hollow Cylinder:

\({I_Z} = J = \frac{{\pi \left( {{D^4} - {d^4}} \right)}}{{32}}\)

where outer diameter = D and inner diameter = d

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Q1.For a symmetrical T-section, the moment of inertia through centroidal axes in its plane parallel to the flange Ixx = 2 × 107 mm4, and perpendicular to the flange is Iyy = 1.5 × 107mm4. The moment of inertia about the centroidal axis normal to the planar area works out to (in mm4):
Q2.A symmetrical I-section has a moment of inertia about the centroidal axis in its plane perpendicular to the web, of 22.34 × 104 mm4. The moment of inertia of the full rectangular area occupied by the I-beam cross section about this axis is 65 × 104 mm4. The two empty spaces on either side of the web are square. What is the height of the web?
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Q6.A symmetrical planar built-up section consists of two channel sections joined together at the tips of their flanges to form a closed rectangular area. The total width of each flange is ‘B’. Each web is ‘w’ units deep inside, ‘D’ units deep at its outside (longer) face, and ‘b' units thick. The moment of inertia of the composite section about its centroidal axis perpendicular to the webs is given by:
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Q1.What is a characteristic of a coplanar parallel force system?
Q2.Which of the following options best describes non-coplanar concurrent forces?
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Q4.Which of the following happens when two equal and opposite forces are applied at a point on a rigid body?
Q5.A symmetrical I-section has a moment of inertia about the centroidal axis in its plane perpendicular to the web, of 22.34 × 104 mm4. The moment of inertia of the full rectangular area occupied by the I-beam cross section about this axis is 65 × 104 mm4. The two empty spaces on either side of the web are square. What is the height of the web?
Q6.When two equal forces F act at an angle θ, the resultant force is given by which of the following expressions?
Q7.A beam with a symmetrical T section has a top flange 50 mm wide and 20 mm thick, and a web 40 mm high and 10 mm thick. An additional plate, 10 mm thick and 60 mm wide, is welded above the flange. The moment of inertia of this symmetrical planar cross- section about an axis in its plane normal to the web and in line with the upper face of the 10 mm thick plate works out to 1506,666.66 mm4. The centroidal axis of the combined area is 21.5 mm below this axis, normal to the web. The moment of inertia of this built-up area about the centroidal axis is (in mm4):
Q8.Which of the following beams is classified as a statically determinate beam?
Q9.The radius of gyration about the polar axis of a circular lamina of radius 0.2 m is:
Q10.How is the resultant force calculated if two forces act along the same straight line but in opposite directions?
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