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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.
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
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