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.
V_{1} = Volume of cylinder = π a^{ 2} × 2 a = 2 π a^{3}
V_{2} = Volume of sphere=(4/3) π a^{3}
Total volume = V_{1} + V_{2} = V (say)
If G is the centre of gravity of the combined body, then OG = y¯
V y¯ = V_{1} y_{1} + V_{2} y_{2}
π a3 [2 + (4/3)] y¯ = π a^{3 } [2 × a] + π a3 × ((4/3)× 3a)
= π a^{3} [2 a + 4 a]
∴ y = 6 a / (2 + (4 /3)) = 6 a / (10/3)
= 1.8 a