Find out the centre of gravity of solid sphere:

Find out the C. G. of a body formed by a solid sphere placed over a solid cylinder of similar radius a as illustrated in Figure, where a = 20 cm.

Solution

Let y axis to be vertically along with the axis of cylinder with centre O of its base as origin.

V₁ = Volume of cylinder = π a ² × 2 a =  2 π a³

V₂ = Volume of sphere=(4/3)  π a³

Total volume = V₁ + V₂ = V (say)

 If G is the centre of gravity of the combined body, then OG =  y¯

V y¯ = V₁  y₁ + V₂  y₂

π a3   [2 +  (4/3)]  y¯ = π a³  [2 × a] + π a3 × ((4/3)× 3a)

=  π a³ [2 a + 4 a]

∴ y = 6 a / (2 +  (4 /3)) =     6 a / (10/3)

= 1.8 a