Question

▶ Derive the equation of COM of Solid Hemisphere!_

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Answer 1

HEY THERE!_

:EQUATION OF COM OF SOLID HEMISPHERE:

Ycom = 3R/8 (due to symmetry Xcom lies at the middle i.e, at centre)

(Refer attachment)

Answer 2

C.O.M of solid hemisphere:

M.R →3R/8 = Y com :

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→ Ycom = ∫ydm / ∫ydm

→ P = Mass / Voume = M/V

→ P = 3M / 2πr³

→ P = dm/dv

→ dm = Pdv = P (2πr²)dr

→ y = r/2

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r

→ Ycom = ∫ 6/2 × P × 2 πr² × r / m

o

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r

→ Pm/M ∫ r³ dr

o

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→ 3Mπ / 2πr¹m [ R^4 / 4 ]

▶Y com = 3R/8

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Y com = 3R/8 = symmetry Y com lies at the centre.

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