An inverted funnel of base radius and height is placed on a smooth horizontal table and is being filled with a liquid of density . It is seen that the liquid starts leaking out from the bottom of the funnel when the height of the liquid is times the height of the conical part of the funnel i.e. .
If the mass of the funnel is m (in kg), then find .
( denotes the greatest integer less than or equal to )
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The normal force acting on the base of the funnel due to the water will be
N = h ρ g π r 2
This normal force will balance the water's weight as well as the weight of the funnel.
N = m w g + m f g .
As m w = [ 3 π r 2 H - 4 ∗ 1 6 ∗ 3 π r 2 H ] ρ
m w = 6 4 2 1 π r 2 H ρ
Therefore m f = 4 3 H ρ π r 2 − 6 4 2 1 H ρ π r 2 = 6 4 2 7 H ρ π r 2
Putting in the values we get m f = 1 . 2 2 k g
Therefore ⌊ m ⌋ = 1