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

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

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

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

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

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

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

Which of the following is/are not true for a triangular pyramid? (a) Triangular pyramid has six faces. (b) Triangular pyramid has four vertices. (c) Triangular pyramid has six edges. (d) The sum of the number of faces, vertices and edges of a triangular pyramid is 14. (e) Triangular pyramid is also known as a tetrahedron.

A

Only (a)

B

Only (b)

C

Only (b) and (c)

D

Only (e)

The moment of inertia of a body about an axis passing through the center of mass is Icm. If the mass of the body is m, find the moment of inertia about an axis parallel to the center of mass and at a distance of R from it.

A

I = Icm = MR2

B

I = I_cm + MR²

C

I = Icm × MR2

D

I = Icm - MR2

Consider the following statement: A ray of light passing through the optical centre of a convex lens emerges without any deviation after refraction. A ray of light passing through the first principal focus of a convex lens emerges parallel to the principal axis after refraction. A ray of light passing through the optical centre of a convex lens emerges parallel to the principal axis after refraction. Which one of the following statements INCORRECT?

A

Only 1

B

Only 2

C

Only 3

D

All 1, 2 and 3

What is the moment of inertia of a triangular section about an axis passing through C.G. and parallel to the base?

A

bh3/12

B

bh3/24

C

bh3/36

D

bh3/6

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

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