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 <img src="/images/question-image/mechanical-engineering/engineering-mechanics/1528353535-11.jpg" title="Engineering Mechanics mcq question image" alt="Engineering Mechanics mcq question image">

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

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

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

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

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

The centre of gravity of the trapezium as shown in below figure from the side is at a distance of

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

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

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

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

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

In the shaded area

In the hole

At ‘O’

None of these

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

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

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

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

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

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

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

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

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

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

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

50 kg

750 kg

100 kg

120 kg

The beam shown in below figure is supported by a hinge at ‘A’ and a roller at ‘B’. The reaction RA of the hinged support ‘A’ of the beam, is

10.8 t

10.6 t

10.4 t

10.2 t

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

0.5 m/sec2

0.75 m/sec2

1.00 m/sec2

1.25 m/sec2

Two loads of 50 kg and 75 kg are hung at the ends of a rope passing over a smooth pulley shown in below figure. The tension in the string is:

50 kg

75 kg

25 kg

60 kg

The ratio of the reactions RA and RB of a simply supported beam shown in below figure is

0.50

0.40

0.67

1.00

The vertical reaction at the support ‘A’ of the structure shown in below figure, is

1 t

2 t

3 t

3.5 t