COMEDK 2023 Shift 1 Paper

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=1cm2
Initial velocity as V1=2m∕ s
Final 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+2gh
where
g=10m∕ s2 is the acceleration due to gravity,
h=20‌cm=0.2m is the height the water has fallen,
Let's calculate V2 :
Now, using the equation of continuity A1V1=A2V2, we can find A2 :
‌1⋅2=A2⋅2√2
‌A2=‌

2

2√2

=‌

1

√2

=‌

√2

2

cm2
Since √2≈1.414, substituting this value gives us:
A2≈‌

1.414

2

cm2≈0.707cm2
Therefore, the cross-sectional area of the stream 20‌cm below the tap is approximately 0.707cm2, making the correct option C) 0.707cm2.