Moment of inertia of a hollow rectangular section as shown in the below figure about X-X axis, is<br><img src="/images/question-image/mechanical-engineering/engineering-mechanics/1528353467-6.jpg" title="Engineering Mechanics mcq question image" alt="Engineering Mechanics mcq question image">

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

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

Moment of inertia of a hollow circular section, as shown in the below figure about an axis perpendicular to the section, is ________ than that about X-X axis.
Engineering Mechanics mcq question image

Engineering Mechanics mcq question image

A

Two times

B

Same

C

Half

D

None of these

Moment of inertia of a hollow circular section, as shown in the below figure about X-axis, is
Engineering Mechanics mcq question image

A

$$\frac{\pi }{{16}}\left( {{{\text{D}}^2} - {{\text{d}}^2}} \right)$$

B

$$\frac{\pi }{{16}}\left( {{{\text{D}}^3} - {{\text{d}}^3}} \right)$$

C

$$\frac{\pi }{{32}}\left( {{{\text{D}}^4} - {{\text{d}}^4}} \right)$$

D

$$\frac{\pi }{{64}}\left( {{{\text{D}}^4} - {{\text{d}}^4}} \right)$$

The moment of inertia of the shaded portion of the area shown in below figure about the X-axis, is
Applied Mechanics and Graphic Statics mcq question image

Applied Mechanics and Graphic Statics mcq question image

A

229.34 cm⁴

B

329.34 cm⁴

C

429.34 cm⁴

D

529.34 cm⁴

A particle of mass m is attached to a thin uniform rod of length a and mass 4m. The distance of the particle from the centre of mass of the rod is $$\frac{a}{2}.$$
Classical Mechanics mcq question image

The moment of inertia of the combination about an axis passing through a normal to the rod is

A

$$\frac{{64}}{{48}}m{a^2}$$

B

$$\frac{{91}}{{48}}m{a^2}$$

C

$$\frac{{27}}{{48}}m{a^2}$$

D

$$\frac{{51}}{{48}}m{a^2}$$

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 the force ‘P’ about ‘O’ as shown in the below figure is
Engineering Mechanics mcq question image

A

P × OA

B

P × OB

C

P × OC

D

P × AC

A vertically immersed surface is shown in the below figure. The distance of its centre of pressure from the water surface is
Hydraulics and Fluid Mechanics in ME mcq question image

Hydraulics and Fluid Mechanics in ME mcq question image

A

$$\frac{{{\text{b}}{{\text{d}}^2}}}{{12}} + \overline {\text{x}} $$

B

$$\frac{{{{\text{d}}^2}}}{{12\overline {\text{x}} }} + \overline {\text{x}} $$

C

$$\frac{{{{\text{b}}^2}}}{{12}} + \overline {\text{x}} $$

D

$$\frac{{{{\text{d}}^2}}}{{12}} + \overline {\text{x}} $$

A circular hole of 50 mm diameter is cut out from a circular disc of 100 mm diameter as shown in the below figure. The center of gravity of the section will lie
Engineering Mechanics mcq question image

A

In the shaded area

B

In the hole

C

At ‘O’

D

None of these

Moment of inertia of a hollow rectangular section as shown in the below figure about X-X axis, is

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