The moment of inertia of a triangular section (base b, height h) about centroidal axis parallel to the base, is

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

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

A rectangle 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 center of gravity and parallel to base is ___________

A

3

B

4

C

12

D

9

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 of a triangular section of base (b) and height (h) about an axis passing through its vertex and parallel to the base, is __________ than that passing through its C.G. and parallel to the base.

A

Nine times

B

Six times

C

Four times

D

Two times

The ratio of moments of inertia of a triangular section about its base and about a centroidal axis parallel to its base, is

A

1.0

B

1.5

C

2.0

D

3.0

The ratio of the moment of inertia of a rectangle about its centroidal axis to the moment of inertia about its base, is

A

$$\frac{1}{4}$$

B

$$\frac{1}{2}$$

C

$$\frac{3}{4}$$

D

$$2$$

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

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

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

In order to have a connecting rod equally strong in buckling about X-axis and Y-axis, the moment of inertia about X-axis should be __________ the moment of inertia about Y-axis.

A

Equal to

B

Twice

C

Three times

D

Four times

Moment of inertia of a triangular section of base (b) and height (h) about an axis passing through its C.G. and parallel to the base, is

A

$$\frac{{{\text{b}}{{\text{h}}^3}}}{4}$$

B

$$\frac{{{\text{b}}{{\text{h}}^3}}}{8}$$

C

$$\frac{{{\text{b}}{{\text{h}}^3}}}{{12}}$$

D

$$\frac{{{\text{b}}{{\text{h}}^3}}}{{36}}$$

The moment of inertia of a triangular section (base b, height h) about centroidal axis parallel to the base, is

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