Moment of Inertia and Centroid MCQ Quiz in मल्याळम - Objective Question with Answer for Moment of Inertia and Centroid - സൗജന്യ PDF ഡൗൺലോഡ് ചെയ്യുക

Last updated on Mar 10, 2025

നേടുക Moment of Inertia and Centroid ഉത്തരങ്ങളും വിശദമായ പരിഹാരങ്ങളുമുള്ള മൾട്ടിപ്പിൾ ചോയ്സ് ചോദ്യങ്ങൾ (MCQ ക്വിസ്). ഇവ സൗജന്യമായി ഡൗൺലോഡ് ചെയ്യുക Moment of Inertia and Centroid MCQ ക്വിസ് പിഡിഎഫ്, ബാങ്കിംഗ്, എസ്എസ്‌സി, റെയിൽവേ, യുപിഎസ്‌സി, സ്റ്റേറ്റ് പിഎസ്‌സി തുടങ്ങിയ നിങ്ങളുടെ വരാനിരിക്കുന്ന പരീക്ഷകൾക്കായി തയ്യാറെടുക്കുക

Latest Moment of Inertia and Centroid MCQ Objective Questions

Top Moment of Inertia and Centroid MCQ Objective Questions

Moment of Inertia and Centroid Question 1:

The radius of gyration of rectangular section (depth D, width B) from a centroidal axis parallel to the width is

  1. D/2
  2. D/√3
  3. D/(2√3)
  4. D/(4√3)

Answer (Detailed Solution Below)

Option 3 : D/(2√3)

Moment of Inertia and Centroid Question 1 Detailed Solution

Concept:

A radius of gyration is given by:

\(r = \sqrt {\frac{I}{A}} \)

I = Moment of inertia about C.G

A = Area of the x-section

\(I = \frac{{B{D^3}}}{{12}}\)

A = BD

\(r = \sqrt {\frac{{B{D^3}}}{{12 \times BD}}}\)

\(r = \frac{D}{{2\sqrt 3 }}\)

Moment of Inertia and Centroid Question 2:

The ______ theorem is used to calculate the moment of inertia of any section about the axis which is different from the axis passing through the centroid in the same plane.

  1. Cross axis theorem
  2. Equal axis theorem
  3. Perpendicular axis theorem 
  4. Parallel axis theorem

Answer (Detailed Solution Below)

Option 4 : Parallel axis theorem

Moment of Inertia and Centroid Question 2 Detailed Solution

Explanation:

Parallel axis theorem: 

The moment of inertia of a body about an axis parallel to the body passing through its center is equal to the sum of moment of inertia of the body about the axis passing through the center in the same plane and product of the mass of the body times the square of the distance between the two axes.

F1 J.S 27.6.20 Pallavi D3

I = Icom + Mx2, Where I is the total moment of inertia of the body, Icom is the moment of inertia about the centre of mass, M is mass, x is the perpendicular distance from an axis passing from centre of mass.

Additional Information

Perpendicular axis theorem: 

This theorem states that the moment of inertia of a plane lamina about an axis perpendicular to its plane is equal to the sum of its moments of inertia about two perpendicular axes concurrent with perpendicular axis and lying in the plane of the body.

F3 J.S 6.6.20 Pallavi D15

Hence it can be expressed as \({I_z} = {I_y} + {I_x}\)

Here Ix, Iand Iare the moment of inertia of an object along X, Y and Z- axis respectively

Moment of Inertia and Centroid Question 3:

Mass moment of inertia of a uniform thin rod of mass (m) and length (l) about its mid-point and perpendicular to its length is

  1. 2/3 ml2
  2. ml2 /12
  3. ml2/3
  4. 3/4 ml2

Answer (Detailed Solution Below)

Option 2 : ml2 /12

Moment of Inertia and Centroid Question 3 Detailed Solution

Mass moment of inertia of a uniform thin rod of mass (m) and length (l) about its mid-point and perpendicular to its length is ml2 /12. 

F1 S.S Shashi 30.07.2019 D3

Moment of Inertia and Centroid Question 4:

Moment of inertia of a triangular section of the base (b) and height (h) about an axis passing through the base, is

  1. \(\frac{bh^3}{4}\)
  2. \(\frac{bh^3}{8}\)
  3. \(\frac{bh^3}{12}\)
  4. \(\frac{bh^3}{36}\)

Answer (Detailed Solution Below)

Option 3 : \(\frac{bh^3}{12}\)

Moment of Inertia and Centroid Question 4 Detailed Solution

RRB JE CE 37 15Q Mechanics Chapter Test(Hindi) - Final images Q1

Moment of Inertia of the triangular section about an axis through its CG and parallel to the base:

\({I_G} = {I_{x'x'}} = \frac{{b{h^3}}}{{36}}\)

Applying Parallel Axis Theorem:

\({I_{BC}} = {I_{x'x'}} + Area\;of\;triangle \times {\left( {\frac{h}{3}} \right)^2}\)

\({I_{BC}} = \frac{{b{h^3}}}{{36}} + \left( {\frac{1}{2} \times b \times h} \right) \times {\left( {\frac{h}{3}} \right)^2}\)

\({I_{BC}} = \frac{{b{h^3}}}{{36}} + \frac{{b{h^3}}}{{18}}\)

\({I_{BC}} = \frac{{b{h^3} + 2b{h^3}}}{{36}} = \frac{{3b{h^3}}}{{36}} = \frac{{b{h^3}}}{{12}}\)

Moment of Inertia and Centroid Question 5:

For the section shown in the figure, the neutral axis lies at:

quesOptionImage2604

  1. \({L \over 3}\)from the top
  2. \({L \over 12}\)from the top
  3. \({5L \over 12}\)from the top
  4. \({7L \over 12}\)from the top

Answer (Detailed Solution Below)

Option 3 : \({5L \over 12}\)from the top

Moment of Inertia and Centroid Question 5 Detailed Solution

Concept:

F1 Ram Singh 28.6.21 Pallavi D5

For Neutral axis

\(̅{y}=\frac{A_{1}× y_{1}+A_{2}× y_{2}}{A_{1}+A_{2}}\)

Taking bottom section as reference

where, A1 = L × L/2

A2 = L/2 × L/2 

y1 = (L/2 + L/4) = 3L/4

y2 = L/4

\(̅{y}=\frac{\left [ (L× \frac{L}{2})(\frac{3L}{4})+(\frac{L}{2}× \frac{L}{2})(\frac{L}{4}) \right ]}{\left ( L× \frac{L}{2}+\frac{L}{2}× \frac{L}{2} \right )}\)

y̅ = \({7L \over 12}\) from bottom 

So, neutral axis from top, y̅' = \(L\;-{7L \over 12}={5L\over 12}\)

Moment of Inertia and Centroid Question 6:

Locate the centroid with respect to base AB of a rectangular section shown in the figure. Consider that a part of the circular section with diameter 150 mm is removed.
F3 Vinanti Engineering 07.12.23 D4

  1. 129.1 mm
  2. 133.68 mm
  3. 1.5.49 mm
  4. 112.44 mm

Answer (Detailed Solution Below)

Option 1 : 129.1 mm

Moment of Inertia and Centroid Question 6 Detailed Solution

Concept:

The centroid of the section shown in the question = qImage658476a19245e2768cf2be4d

Where, 

y1 is the distance centroid of the rectangle from base AB

y2 is the distance centroid of the circle from base AB

Explanation:

Given, 

Area of rectangle = 300 x 200 = 60000 mm2

The centroid of the rectangle from AB = 150 mm

Area of circle = \( \frac{\pi }{4}\)x15017671.46 mm2

The centroid of the circle from AB = 300-100 = 200 mm

Thus, Centroid = qImage658476a19245e2768cf2be4d\( \frac{60000*150-17671.46*200 }{60000-17671.46}\)=129.1 mm

 

Moment of Inertia and Centroid Question 7:

Moment of inertia of a square of side a about the diagonal is

  1. \(\frac {a^4}{18}\)
  2. \(\frac {a^4}{24}\)
  3. \(\frac {a^4}{12}\)
  4. \(\frac {a^4}{8}\)

Answer (Detailed Solution Below)

Option 3 : \(\frac {a^4}{12}\)

Moment of Inertia and Centroid Question 7 Detailed Solution

Explanation:

MOI for a Triangle:

F1 Ateeb 8-12-2020 Swati D1

About centroidal axis: \(I_G=\frac{bh^3}{36}\)

About base: \(I_{BC}=\frac{bh^3}{12}\)

A square can be divided into two triangles about its base.

Diagonal of square = Base of the triangle (b) = \(a\sqrt{2}\)

Height of triangle = Half of square diagonal (h) = \(\frac{a}{\sqrt{2}}\)

MOI of the square about the diagonal:

\(I_{square}=2\times \left(I_{triangle}\right)_{base}\)

\(I_{square}=2\times \frac{bh^3}{12}\)

\(I_{square}=2\times \frac{(a\sqrt{2})\left(\frac{a}{\sqrt{2}}\right)^3}{12}\)

\(I_{square}=\frac{a^4}{12}\ \)

Moment of Inertia and Centroid Question 8:

What is the moment of inertia of the given I section about its centroidal axis?

F1 Ashik 1.12.20 Pallavi D11 Corrected(Ravi) 21.10.21

  1. 152/3t4
  2. 16/3t4 
  3. 56 t4
  4. 56 t3

Answer (Detailed Solution Below)

Option 3 : 56 t4

Moment of Inertia and Centroid Question 8 Detailed Solution

Concept:

Moment of inertia of Rectangle about each of its centroidal axis is:

\({{\bf{I}}_{{\bf{xx}}}} = \frac{{{\bf{b}}{{\bf{d}}^3}}}{{12}}\;{\bf{and}}\;{{\bf{I}}_{{\bf{yy}}}} = \frac{{{\bf{d}}{{\bf{b}}^3}}}{{12}}\)

where b = width of the rectangle, h = height of the rectangle

ee

Moment of inertia of the I section can be calculated by calculating the Moment of inertia of the rectangular section shown below

F1 Ateeb Anil 21.12.20  D3

Now the Moment of inertia of I section = Moment of inertia of rectangle section 1 - (2 × Moment of inertia of rectangle Section 2)

Calculation:

Given:

b1 = 4t, d1 = 6t, \(b_2 = (2t-\frac{t}{2})=1.5t\), d2 = (6t - t - t ) = 4t

where b1 = width rectangle section 1, b2 = width rectangle section 2, d1 = height rectangle section 1, d1 = height rectangle section 2

\(Moment\ of\ inertia\ of\ I\ section= \frac{b_1d_1^3}{12}-(2\times\frac{b_2d_2^3}{12})\)

\(Moment\ of\ inertia\ of\ I\ section= \frac{4t×(6t)^3}{12}-(2\times\frac{1.5t×(4t)^3}{12})\)

\(Moment\ of\ inertia\ of\ I\ section= 72t^4-{16t^4}\)

\(Moment\ of\ inertia\ of\ I\ section= 56t^4\)

Moment of Inertia and Centroid Question 9:

Moment of inertia (second moment of area) of triangular lamina about base and centroidal axis (parallel to base), respectively will be ______ and _______ [ b = length of base of triangular section, h = Height of triangular section]

  1. \(\frac{{b{h^3}}}{3},\frac{{b{h^3}}}{{36}}\)
  2. \(\frac{{b{h^3}}}{{36}},\frac{{b{h^3}}}{{12}}\)
  3. \(\frac{{b{h^3}}}{{12}},\frac{{b{h^3}}}{{36}}\)
  4. \(\frac{{b{h^3}}}{3},\frac{{b{h^3}}}{{12}}\)

Answer (Detailed Solution Below)

Option 3 : \(\frac{{b{h^3}}}{{12}},\frac{{b{h^3}}}{{36}}\)

Moment of Inertia and Centroid Question 9 Detailed Solution

Concept:

Moment of inertia of a triangle with base b and height h

\({I_{base}} = \frac{{b{h^3}}}{{12}}\)

Parallel axis theorem

Parallel axis theorem is used to find a moment of inertia about an axis which is at some distance from the centroidal axis and parallel to centroidal.

Suppose an axis is at distance d from the centroidal axis and parallel to the centroidal axis.

according to the parallel axis theorem, the moment of inertia about that axis is given by,

\({I_{about~axis~parallel~to~centroida~laxis}} = {I_{about~centroidal~axis}} + A{d^2}\)

Moment of inertia about the centroidal axis of the triangle

F1 Ashik Madhu 14.08.20 D15

Applying parallel axis theorem we get

\({I_{xx}} = {I_{cc}} + A{\left( {\frac{h}{3}} \right)^2}\)

\({I_{cc}} = {I_{xx}} - A{\left( {\frac{h}{3}} \right)^2}\)

\(I_{cc}=\frac{{b{h^3}}}{{12}} - \frac{{bh}}{2} \times \frac{{{h^2}}}{9} = \frac{{b{h^3}}}{{36}}\)

\({I_{centroid}} = \frac{{b{h^3}}}{{36}}\)

Moment of Inertia and Centroid Question 10:

Calculate the value of y̅ (distance from line 'Ox' to centroid) for the I-section shown in the figure.
F1 Vinanti Engineering 09.08.23 D16

  1. 44.44 mm
  2. 32.24 mm
  3. 58.26 mm
  4. 52.56 mm

Answer (Detailed Solution Below)

Option 1 : 44.44 mm

Moment of Inertia and Centroid Question 10 Detailed Solution

Concept:

Centre of gravity of plane figures (T-sections, I-sections, L-sections, etc.)

The plane geometrical figures (such as T-section, I-section, L-section etc.) have only areas but no mass. The centre of gravity of such figures is found out in the same way as that of solid bodies. The centre of area of such figures is known as centroid and coincides with the centre of gravity of the figure. It is a common practice to use the centre of gravity for centroid and vice versa.

Let \(\bar x\) and \(\bar y\) be the co-ordinates of the centre of gravity with respect to some axis of reference, then

\(\bar y={A_1y_1+A_2y_2+A_3y_3+.....+A_ny_n\over A_1+A_2+A_3+.....+A_n}={{\sum_{i=1}^{i=n}A_iy_i}\over \sum_{i=n}^{i=n}A_i}\)

\(\bar x={A_1 x_1+A_{2} x_2+A_3 x_{3}+.....+A_n x_n\over A_1+A_2+A_3+.....+A_n}={{\sum_{i=1}^{i=n}A_i x_i}\over \sum_{i=n}^{i=n}A_i}\)

where A1, A2, A3........ etc., are the areas into which the whole figure is divided x1, x2, x3 ..... etc., are the respective coordinates of the areas A1, A2, A3....... on X-X axis with respect to same axis of reference.
y1, y2, y3....... etc., are the respective coordinates of the areas  A1, A2, A3....... on the Y-Y axis with respect to the same axis of the reference.

Calculation:

Given
F1 Vinanti Engineering 09.08.23 D16

\(\bar y={A_1y_1+A_2y_2+A_3y_3\over A_1+A_2+A_3}\)

\(A_1 =800\, mm^2\, y_1=69\, mm\)

\(A_2=400 \, mm^2\, y_2=44\, mm\)

\(A_3=600 \, mm^2\, y_3=12\, mm\)

\(\bar y={800\times 69+400\times 44+600\times 12\over 800+400+600}\)

\(\bar y={80000\over 1800}=44.44\, mm\)

\(\bar y=44.44\, mm\)

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