The moment of inertia of a rectangular section 3 cm wide and 4 cm deep about X-X axis passing through center is ____

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RRB JE ME CBT 2 Previous Paper 1: Held on 29 Aug 2019
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  1. 20 cm4
  2. 12 cm4
  3. 9 cm4
  4. 16 cm4

Answer (Detailed Solution Below)

Option 4 : 16 cm4
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Concept:

Area Moment of Inertia:

  • It is a geometrical property of an area which reflects how its points are distributed with regards to an arbitrary axis.
  • It is also known as 2nd moment of area or 2nd Moment of Inertia.
  • Its SI unit is ‘m4
  • Mathematically, it is represented as

\({I_x} = \int\!\!\!\int {y^2}\;dxdy\;\;and\;\;\;{I_y} = \int\!\!\!\int {x^2}dxdy\)

Calculation:

Given:

width(b) = 3 cm, height(h)= 4 cm

For the rectangular section, the Moment of Inertia is given by

\({I_{xx}} = \frac{{b{h^3}}}{{12}} = \frac{{3 \times {4^3}}}{{12}} = 16\;c{m^4}\)

26 June 1

Mass Moment of Inertia:

It is a measure of the resistance of a body to angular acceleration about a given axis that is equal to the sum of the products of each element of mass in the body and the square of the element’s distance from the axis.

It’s SI unit is kg-m2

Mathematically, \(I = \mathop \sum \limits_{i = 1}^n {m_i}r_i^2\)

MOI of Some Standard Shapes:

Type of Shape

Moment of Inertia

Rectangle

\({I_{xx}} = \frac{{b{h^3}}}{{12}},\;\;{I_{yy}} = \frac{{h{b^3}}}{{12}}\)

Triangle

\({I_{C.G}} = \frac{{b{h^3}}}{{36}}\;,\;{I_{base}} = \frac{{b{h^3}}}{{12}}\)

Circle

\({I_{xx}} = {I_{yy}} = \frac{\pi }{{64}}{d^4}\)

Semicircle

\({I_{xc}} = 0.393{r^4}\;,\;\;\;{I_{yc}} = 0.11{r^4}\)

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