Moment of Inertia about an inclined axis is the integration of the cube of the distance of the centroid and the del area along the whole area of the structure and after this calculations, we multiply the moment of areas.

Moment of Inertia about an inclined axis is the integration of the square of the distance of the centroid and the del area along the whole area of the structure and after this calculations, we multiply the moment of areas.

A

True

B

False

Moment of Inertia is the integration of the square of the distance of the centroid and the del area along the whole area of the structure and after these calculations, we multiply the moment of areas.

A

True

B

False

Moment of Inertia is the integration of the square of the distance of the centroid and the del area along the whole area of the structure and this moment is at a distance from the rotating axis, known as the radius of gyration.

A

True

B

False

Which one of the following four addresses is NOT EXACTLY same as the one given below? Annalise Anna AV. Vicente Guerrero NTE. 3499, del Norte, 64500 Monterrey, N.L., Mexico (i) Annalise Anna AV. Vicente Guerrero NTE. 3499, del Norte, 64500 Monterrey, N.L., Mexico (ii) Annalise Anna AV. Vicente Guerrero NTE. 3499, del Norte, 64500 Monterrey, N.L., Mexico (iii) Annalise Anna AV. Vicente Guerrero NTE. 3499, del Norte, 64500 Monterrey, N.L., Mexico (iv) Annalise Anna AU. Vicente Guerrero NTE. 3499, del Norte, 64500 Monterrey, N.L., Mexico

A

iv

B

i

C

ii

D

iii

Moment of Inertia is the integration of the square of the distance of the centroid and the del area along the whole area of the structure.

A

True

B

False

According to parallel axis theorem, the moment of inertia of a section about an axis parallel to the axis through center of gravity (i.e. $$I$$P) is given by (where, A = Area of the section, $$I$$G = Moment of inertia of the section about an axis passing through its C.G. and h = Distance between C.G. and the parallel axis.)

A

$$I{\text{P}} = I{\text{G}} + {\text{A}}{{\text{h}}^2}$$

B

$$I{\text{P}} = I{\text{G}} - {\text{A}}{{\text{h}}^2}$$

C

$$I{\text{P}} = \frac{{I{\text{G}}}}{{{\text{A}}{{\text{h}}^2}}}$$

D

$$I{\text{P}} = \frac{{{\text{A}}{{\text{h}}^2}}}{{I{\text{G}}}}$$

According to parallel axis theorem, the moment of inertia of a section about an axis parallel to the axis through center of gravity (i.e. $${I_{\text{P}}}$$) is given by (where, A = Area of the section, $${I_{\text{G}}}$$ = Moment of inertia of the section about an axis passing through its C.G. and h = Distance between C.G. and the parallel axis.)

A

$${I_{\text{P}}} = {I_{\text{G}}} + {\text{A}}{{\text{h}}^2}$$

B

$${I_{\text{P}}} = {I_{\text{G}}} - {\text{A}}{{\text{h}}^2}$$

C

$${I_{\text{P}}} = \frac{{{I_{\text{G}}}}}{{{\text{A}}{{\text{h}}^2}}}$$

D

$${I_{\text{P}}} = \frac{{{\text{A}}{{\text{h}}^2}}}{{{I_{\text{G}}}}}$$

The parallel axis theorem can add any angle varied moment of inertias to give the perpendicular moment of inertia and it can be used in the determination of the moment of inertia about inclined axis.

A

True

B

False

The moment of inertia of a uniform sphere of radius, r about an axis passing through its centre is given by $$\frac{2}{5}\left( {\frac{{4\pi }}{3}{r^5}\rho } \right).$$ A rigid sphere of uniform mass density $$\rho $$ and radius R has two smaller spheres of radii $$\frac{R}{2}$$ hollowed out of it as shown in the figure given below.
Classical Mechanics mcq question image

The moment of inertia of the resulting body about Y-axis is

A

$$\frac{{\pi \rho {R^5}}}{4}$$

B

$$\frac{{5\pi \rho {R^5}}}{{12}}$$

C

$$\frac{{7\pi \rho {R^5}}}{{12}}$$

D

$$\frac{{3\pi \rho {R^5}}}{4}$$

A triangle is having base b and height h. The ratio of the moment of inertia when axis is passing through its base to moment of inertia of when axis passing through centroid and parallel to base is ______

A

3

B

6

C

12

D

9

Moment of Inertia about an inclined axis is the integration of the cube of the distance of the centroid and the del area along the whole area of the structure and after this calculations, we multiply the moment of areas.

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