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.<br> <img src="/images/question-image/mechanical-engineering/engineering-mechanics/1528353415-5.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 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

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

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

A

$$\frac{{{\text{B}}{{\text{D}}^3}}}{{12}} - \frac{{{\text{b}}{{\text{d}}^3}}}{{12}}$$

B

$$\frac{{{\text{D}}{{\text{B}}^3}}}{{12}} - \frac{{{\text{d}}{{\text{b}}^3}}}{{12}}$$

C

$$\frac{{{\text{B}}{{\text{D}}^3}}}{{36}} - \frac{{{\text{b}}{{\text{d}}^3}}}{{36}}$$

D

$$\frac{{{\text{D}}{{\text{B}}^3}}}{{36}} - \frac{{{\text{d}}{{\text{b}}^3}}}{{36}}$$

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 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

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

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

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.

A

Two times

B

Same

C

Half

D

None of these

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 mass m is constrained to move on a horizontal frictionless surface. It is set in circular motion with radius r₀ and angular speed ω₀ by an applied force $$\overrightarrow {\bf{F}} $$ communicated through an inextensible thread that passesthrough a hole on the surface as shown in figure given below. Then, this force is suddenly doubled.
Classical Mechanics mcq question image

The magnitude of the radial velocity of the mass

A

increases till mass falls into hole

B

decreases till mass falls into hole

C

remains constant

D

becomes zero at radius r₁, where 0 1 0

A square hole is made in a circular lamina, the diagonal of the square is equal to the radius of the circle as shown in below figure the shift in the centre of gravity is
Applied Mechanics and Graphic Statics mcq question image

A

$$\frac{{{\text{r}}\left( {\pi - 0.75} \right)}}{{\left( {\pi - 0.5} \right)}}$$

B

$$\frac{{{\text{r}}\left( {\pi - 0.25} \right)}}{{\left( {\pi - 0.75} \right)}}$$

C

$$\frac{{{\text{r}}\left( {\pi - 0.5} \right)}}{{\left( {\pi - 0.75} \right)}}$$

D

$$\frac{{{\text{r}}\left( {\pi - 0.5} \right)}}{{\left( {\pi - 0.25} \right)}}$$

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.

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