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The moment of the force ‘P’ about ‘O’ as shown in the below figure is<br> <img src="/images/question-image/mechanical-engineering/engineering-mechanics/1528353506-20.jpg" title="Engineering Mechanics mcq question image" alt="Engineering Mechanics mcq question image">
A
P × OA
B
P × OB
C
P × OC
D
P × AC
Correct Answer:
P × OC
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.
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 r
0
and angular speed ω
0
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.
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 r<sub>1</sub>, 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.
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
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.
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
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
A
229.34 cm<sup>4</sup>
B
329.34 cm<sup>4</sup>
C
429.34 cm<sup>4</sup>
D
529.34 cm<sup>4</sup>
A vertically immersed surface is shown in the below figure. The distance of its centre of pressure from the water surface is
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
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
A
W sinθ
B
W cosθ
C
W secθ
D
W cosecθ