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 <br><img src="/images/question-image/mechanical-engineering/engineering-mechanics/1528353276-9.jpg" title="Engineering Mechanics mcq question image" alt="Engineering Mechanics mcq question image">

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

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

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

Last year, there were three sections in a competitive exam. Out of them 33 students cleared the cut-off in Section A, 34 students cleared the cut-off in Section B and 32 students cleared the cut-off in Section C. 10 students cleared the cut-off in section A and section B, 9 cleared the cut-off in section B and section C and 8 cleared the cut-off in section A and section C. The number of students who cleared only one section was equal and was 21 for each section. How many students cleared all the three sections?

A

6

B

9

C

8

D

7

The center of gravity of a trapezium with parallel sides 'a' and 'b' lies at a distance of 'y' from the base 'b', as shown in the below figure. The value of 'y' is
Engineering Mechanics mcq question image

Engineering Mechanics mcq question image

A

$${\text{h}}\left( {\frac{{2{\text{a}} + {\text{b}}}}{{{\text{a}} + {\text{b}}}}} \right)$$

B

$$\frac{{\text{h}}}{2}\left( {\frac{{2{\text{a}} + {\text{b}}}}{{{\text{a}} + {\text{b}}}}} \right)$$

C

$$\frac{{\text{h}}}{3}\left( {\frac{{2{\text{a}} + {\text{b}}}}{{{\text{a}} + {\text{b}}}}} \right)$$

D

$$\frac{{\text{h}}}{3}\left( {\frac{{{\text{a}} + {\text{b}}}}{{2{\text{a}} + {\text{b}}}}} \right)$$

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

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 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 centre of gravity of the trapezium as shown in below figure from the side is at a distance of
Applied Mechanics and Graphic Statics mcq question image

A

$$\frac{{\text{h}}}{3} \times \frac{{{\text{b}} + {\text{2a}}}}{{{\text{b}} + {\text{a}}}}$$

B

$$\frac{{\text{h}}}{3} \times \frac{{2{\text{b}} + {\text{a}}}}{{{\text{b}} + {\text{a}}}}$$

C

$$\frac{{\text{h}}}{2} \times \frac{{{\text{b}} + {\text{2a}}}}{{{\text{b}} + {\text{a}}}}$$

D

$$\frac{{\text{h}}}{2} \times \frac{{2{\text{b}} + {\text{a}}}}{{{\text{b}} + {\text{a}}}}$$

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 weight of 100 kg is supported by a string whose ends are attached to pegs ‘A’ and ‘B’ at the same level shown in below figure. The tension in the string is
Applied Mechanics and Graphic Statics mcq question image

A

50 kg

B

750 kg

C

100 kg

D

120 kg

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

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

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

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