  Question

Water from a tap emerges vertically down with an initial speed of $$1.0\ ms^{-1}$$. The cross sectional area of tap is $$10\ cm^{2}$$. Assume that the pressure is constant through out the stream of water,and that the flow is steady, the cross sectional area of the steam $$0.15\ m$$ below the tap is

A
5×104 m2  B
5×105 m2  C
5.0×105 m2  D
50×104 m2  Solution

The correct options are A $$5\times 10^{-4}\ m^{2}$$ C $$5.0 \times 10^{-5}\ m^{2}$$Given initial velocity $$u = 1 m s^{-1}$$Area $$A = 10 c m^{2} = 10 \times 10^{-4} m^{2}$$Velocity at height  0.15 m below  the  tap is: $$v^{2} = u^{2} + 2 gh$$                                                                              $$= (1)^{2} + 2\times 10\times 0.1 s$$                                                                              $$= 4$$$$\Rightarrow v = 2 m s^{-1}$$We  know  that  by  continuity  Theoram  $$A_{1}v_{1} = A_{2}v_{2}$$         $$1\times 10\times 10^{-4} = A^{2}\times 2$$                 $$5\times 10^{-4} = A^{2}$$Physics

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