What is not the condition for the equilibrium in three dimensional system of axis for the composite bodies if we are determining the moment of inertia for them?

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 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

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

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

What is not the condition for the equilibrium in three dimensional system of axis for the composite bodies?

A

∑Fx=0

B

∑Fy=0

C

∑Fz=0

D

∑F≠0

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 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

If a disc has moment of inertia I about the axis which is tangential and in plane of the disc. then the moment of inertia about the axis which is tangential and perpendicular to its plane will be

A

$\dfrac{6}{5} I$

B

$\dfrac{3}{4} I$

C

$\dfrac{3}{2} I$

D

$\dfrac{5}{4} I$

If a disc has moment of inertia I about the axis which is tangential and in plane of the disc, then the moment of inertia about the axis which is tangential and perpendicular to its plane will be:

A

$\dfrac{6}{5}I$

B

$\dfrac{3}{4}I$

C

$\dfrac{3}{2}I$

D

$\dfrac{5}{4}I$

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

What is not the condition for the equilibrium in three dimensional system of axis for the composite bodies if we are determining the moment of inertia for them?

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