(^98) A Textbook of Engineering Mechanics

Now we find that the answer obtained is more than the right hand side of equation (i). Thus the

value of (h) is less than 39.5 mm. Now let us substitute the h = 39.4 mm in the left hand side of

equation, (i).

(39.4)^4 – 78.67 (39.4)^3 = – 2 401 900

We find that is answer is very close to the right hand side of the equation and there is no need

of further calculations. Thus the value of h = 39.4 mm Ans.

EXERCISE 6.3

- A circular hole of 50 mm diameter is cut out from a circular disc of 100 mm diameter as

shown in Fig. 6.31. Find the centre of gravity of the section from A.[Ans. 41.7 mm]

`Fig. 6.31. Fig. 6.32.`

- Find the centre of gravity of a semicircular section having outer and inner diameters of 200

mm and 160 mm respectively as shown in Fig. 6.32. [Ans. 57.5 mm from the base] - A circular sector of angle 45° is cut from the circle of radius 220 mm Determine the centre

of gravity of the remainder from the centre of the sector. [Ans. 200 mm] - A hemisphere of radius 80 mm is cut out from a right circular cylinder of diameter 80

mm and height 160 mm as shown in Fig. 6.33. Find the centre of gravity of the body

from the base AB.[Ans. 77.2 mm]

`Fig. 6.33. Fig. 6.34.`

- A right circular cone of 30 mm diameter and 60 mm height is cut from a cylinder of 50

mm diameter at 120 mm height as shown in Fig. 6.34. Find the position of the centre of

gravity of the body from its base. [Ans. 60.7 mm]

QUESTIONS

- Define the terms ‘centre of gravity’.
- Distinguish between centre of gravity and centroid.