Chapter 6 : Centre of Gravity 95

Example 6.17. A frustum of a solid right circular cone has an axial hole of 50 cm diameter

as shown in Fig. 6.28.

Fig. 6.28.

Determine the centre of gravity of the body.

Solution. As the body is symmetrical about vertical axis,

therefore its centre of geravity lie on this axis. For the sake of sim-

plicity, let us assume a right circular cone OCD, from which a right

circulr cone OAB is cut off as shown in Fig. 6.29.

`Let base of cone CD be the axis of reference.`

(i) Right circular cone OCD

2

# vRH (^13)

π

=× ×

(1)^2344 m

33

ππ

=× ×=

and 1

4

1m

4

y ==

(ii) Right circular cone OAB

2

2

3

vrh

π

=××

(0.5)^232 m

36

ππ

=× ×=

and 2

25

2m

42

y =+ =

(iii) Circular hole

223

3 (0.5)^2 m

44 8

vdh

ππ π

=× ×=× ×=

and 2

2

1m

2

y ==

We know that distance between centre of gravity of the body and the base of the cone,

11 2 2 3 3

123

––

––

vy v y v y

y

vv v

# (^45451)

11

(^36283128)

4411

368 368

⎛⎞⎛⎞⎛⎞ππ π

⎜⎟⎜⎟⎜⎟×− × − × −−

⎝⎠⎝⎠⎝⎠

ππ π

−− −−

19

0.76 m

25

== Ans.

Fig. 6.29.