A solid hemisphere is just pressed below the liquid, the value of F 1 F 2 is ( where F 1 and F 2 are the hydrostatic forces acting on the curved and flat surfaces of the hemisphere ) ( Neglect atmospheric pressure )
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The ratio between the forces is 3:1
Explanation:
Density of the liquid = P
Radius = R
R1= ρgR(πR^2 )
- A different ring at depth x from the square of with dx pressure at the period ρgx
- Net downward force m This differential ring
df=ρgx(2πR.dx)sinθ
sinθ= R−x / R
∫df =∫ R-0 ρgx (2πRdx). R−x / R
f2 = 2πρg∫ R-0 x(R−x)dx =2πρg [ Rx^ 2/2 − x^ 3/3 ] R-0
= 2πρg( R^ 3/6 )
f1 / f2 = ρgR (πR^2 ) / 2πρg( R^ 2/6 )
f1 / f2 = 3 : 1
Hence the ratio between the forces is 3:1
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