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.