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Water from a tap emerges vertically downwards with an initial spped of 1.0 m s -1 . Assume that the pressure is constant throughout the stream of water, and that the flow is steady. The cross-sectional area of the stream 0.15 m below the tap is (a) 5.0*10 -4 m 2 (b) 1.0*10 -5 m 2 (c) 5.0 * 10 -5 m 2 (d) 2.0*10 -5 M 2

Water from a tap emerges vertically downwards with an initial spped of 1.0 m s-1. Assume that the pressure is constant throughout the stream of water, and that the flow is steady. The cross-sectional area of the stream 0.15 m below the tap is
(a) 5.0*10-4m2
(b) 1.0*10-5m2
(c) 5.0 * 10-5m2
(d) 2.0*10-5M2

Grade:upto college level

1 Answers

Navjyot Kalra
askIITians Faculty 654 Points
7 years ago
(c) KEY CONCEPT :
The equation of continuity is : v 1A1 = v2A2
where v and A represent the speed of water stream and its area of cross section, respectively. We are given that
v1 = 1.0 ms-1
A1 = 10-4m2
v2 = velocity of water stream at 0.15 m below the tap
A2 = ?
For calculating v2
u = 1 m/s; s = 1.5 m, a = 10m/s2 and v = ?
v2 – u2 = 2as
v2 – 1 = 2*10 * 0.5 \Rightarrowv = 2m/s
Hence, A2 = v1A1/v2 = 1*10-4/2 = 5*10-5m2

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