Q.

There are two identical small holes of area of cross-section a on the opposite sides of a tank containing a liquid of density  ρ. The difference in height between the holes is h. Tank is resting on a smooth horizontal surface. Horizontal force which will has to be applied on the tank to keep it in equilibrium is

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a

ghρa

b

2ghρ a

c

2ρagh

d

ρgha

answer is C.

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Detailed Solution

Net force (reaction) = F=FB−FA=dpBdt−dpAdt                                =avBρ×vB−avAρ×vA∴  F=aρvB2−vA2                        …(i)According to Bernoulli's theorem pA+12ρvA2+ρgh=pB+12ρvB2+0⇒12ρvB2−vA2=ρgh⇒vB2−vA2=2ghFrom equation (i),  F=2aρgh.
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