A vertically immersed surface is shown in the below figure. The distance of its centre of pressure from the water surface is<br><img src="/images/question-image/mechanical-engineering/hydraulics-and-fluid-mechanics-in-me/1664193121-a-vertically-immersed-surface-is-shown-in.jpg" title="Hydraulics and Fluid Mechanics in ME mcq question image" alt="Hydraulics and Fluid Mechanics in ME mcq question image">

The depth of centre of pressure (h) for a vertically immersed surface from the liquid surface is given by (where IG = Moment of inertia of the immersed surface about horizontal axis through its centre of gravity, A = Area of immersed surface, and x = Depth of centre of gravity of the immersed surface from the liquid surface)

A

(IG/Ax̅) - x̅

B

(IG/x̅) - Ax̅

C

(Ax̅/IG) + x̅

D

(IG/Ax̅) + x̅

The depth of centre of pressure (h) for a vertically immersed surface from the liquid surface is given by (where $${I_{\text{G}}}$$ = Moment of inertia of the immersed surface about horizontal axis through its centre of gravity, A = Area of immersed surface and x = Depth of centre of gravity of the immersed surface from the liquid surface)

A

$$\frac{{{I_{\text{G}}}}}{{{\text{A}}\overline {\text{x}} }} - \overline {\text{x}} $$

B

$$\frac{{{I_{\text{G}}}}}{{\overline {\text{x}} }} - {\text{A}}\overline {\text{x}} $$

C

$$\frac{{{\text{A}}\overline {\text{x}} }}{{{I_{\text{G}}}}} + \overline {\text{x}} $$

D

$$\frac{{{I_{\text{G}}}}}{{{\text{A}}\overline {\text{x}} }} + \overline {\text{x}} $$

A block of mass m₁, placed on an inclined smooth plane is connected by a light string passing over a smooth pulley to mass m₂, which moves vertically downwards as shown in the below figure. The tension in the string is
Engineering Mechanics mcq question image

Engineering Mechanics mcq question image

A

$$\frac{{{{\text{m}}_1}}}{{{{\text{m}}_2}}}$$

B

$${{\text{m}}_1}{\text{g}}\sin \alpha $$

C

$$\frac{{{{\text{m}}_1}{{\text{m}}_2}}}{{{{\text{m}}_1} + {{\text{m}}_2}}}$$

D

$$\frac{{{{\text{m}}_1}{{\text{m}}_2}{\text{g}}\left( {1 + \sin \alpha } \right)}}{{{{\text{m}}_1} + {{\text{m}}_2}}}$$

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

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

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

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

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

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

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

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 body A of mass 6.6 kg which is lying on a horizontal platform 4.5 m from its edge is connected to the end of a light string whose other end is supporting a body of mass 3.2 kg as shown in below figure. If the friction between the platform and the body A is $$\frac{1}{3}$$, the acceleration is
Applied Mechanics and Graphic Statics mcq question image

A

0.5 m/sec²

B

0.75 m/sec²

C

1.00 m/sec²

D

1.25 m/sec²

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

A vertically immersed surface is shown in the below figure. The distance of its centre of pressure from the water surface is

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