The moment of the force ‘P’ about ‘O’ as shown in the below figure is

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

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

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

In a framed structure, as shown in the below figure, the force in the member AB is __________ the force in member AC.
Engineering Mechanics mcq question image

A

Half

B

Equal to

C

Double

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

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

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

A

Two times

B

Same

C

Half

D

None of these

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 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

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

The force induced in the string BC due to the load 'W' as shown in the below figure is
Engineering Mechanics mcq question image

A

W sinθ

B

W cosθ

C

W tanθ

D

W cotθ

The force induced in the string AB due to the load W, as shown in the below figure is
Engineering Mechanics mcq question image

A

W sinθ

B

W cosθ

C

W secθ

D

W cosecθ

The moment of the force ‘P’ about ‘O’ as shown in the below figure is

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