Two holes 1 and 2 are made at depths h and 16h respectively. Both the ...
After some time V
1 and V
2 both will decrease, but decrease in the value of V
1 is
more dominating. So
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Two holes 1 and 2 are made at depths h and 16h respectively. Both the ...
Initially, equal volumes of liquid will flow from both holes in unit time. However, after some time, more volume of liquid will flow from hole-2 per unit time. Let's break down the explanation into two parts.
1. Initially equal volumes of liquid will flow from both holes in unit time.
- The volume of liquid flowing through a hole in unit time is directly proportional to the area of the hole.
- The area of a circle is given by the formula A = πr^2, where r is the radius of the circle.
- Let's assume the radius of hole-2 is 'r'. According to the question, the radius of hole-1 is two times that of hole-2, so the radius of hole-1 is 2r.
- Therefore, the area of hole-2 is πr^2 and the area of hole-1 is π(2r)^2 = 4πr^2.
- Since the areas of the holes are directly proportional to the volumes of liquid flowing through them, initially, equal volumes of liquid will flow from both holes in unit time.
2. After some time, more volume of liquid will flow from hole-2 per unit time.
- The flow rate or volume of liquid flowing through a hole is also influenced by the depth of the hole.
- Let's assume the depth of hole-1 is 'h' and the depth of hole-2 is 16h, as given in the question.
- The pressure difference between the top and bottom of a fluid column of height 'h' is given by the equation P = ρgh, where ρ is the density of the liquid and g is the acceleration due to gravity.
- As we can see, the pressure difference depends on the height of the fluid column.
- Since the depth of hole-2 is 16 times greater than that of hole-1, the pressure difference for hole-2 will be 16 times higher than that of hole-1.
- The flow rate of liquid is directly proportional to the pressure difference, so more volume of liquid will flow from hole-2 per unit time.
Therefore, the correct answer is option 'A, D': Initially, equal volumes of liquid will flow from both the holes in unit time, but after some time, more volume of liquid will flow from hole-2 per unit time.