To find the cross-sectional area of the stream
20‌cm below the tap, we can use the equation of continuity which states that for an incompressible and steady flow of fluid, the product of cross-sectional area (A) and the velocity of flow
(V) at any point is constant throughout the flow. We can pair this with the equation that determines the velocity of a freely falling object to address the change in velocity as the water falls.
First, let's denote:
Initial cross-sectional area as
A1=1cm2Initial velocity as
V1=2m∕ sFinal cross-sectional area as
A2, which we need to find.
Final velocity as
V2, which we can find using the formula for the velocity of a freely falling object.
The velocity of a freely falling object can be determined by the formula:
V2=√V12+2ghwhere
g=10m∕ s2 is the acceleration due to gravity,
h=20‌cm=0.2m is the height the water has fallen,
Let's calculate
V2 :
V2=√(2)2+2⋅10⋅0.2=√4+4=√8=2√2m∕ s
Now, using the equation of continuity
A1V1=A2V2, we can find
A2 :
‌1⋅2=A2⋅2√2‌A2=‌=‌=‌cm2Since
√2≈1.414, substituting this value gives us:
A2≈‌cm2≈0.707cm2Therefore, the cross-sectional area of the stream
20‌cm below the tap is approximately
0.707cm2, making the correct option C)
0.707cm2.