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Water is filled up to a height 'h' in a cylindrical vessel. Now, a hole of area 'A' is made at bottom of the vessel. Water drains out of the hole in time 't' seconds. If we repeat the above process with a height of water as '4h', then how much time it require for water to drain out of the cylinder?
[Assume A << A0 (area of tank)]
[Assume A << A0 (area of tank)]
- a)t seconds
- b)4t seconds
- c)2t seconds
- d)t/4 seconds
Correct answer is option 'C'. Can you explain this answer?
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Water is filled up to a height 'h' in a cylindrical vessel. No...
Time required to empty the tank
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Water is filled up to a height 'h' in a cylindrical vessel. No...
Understanding the Problem
When water drains from a hole in a cylindrical vessel, the time it takes to drain is influenced by the height of the water and the area of the hole. We will use Torricelli's Law, which states that the speed of efflux of a fluid under gravity through an orifice is proportional to the square root of the height of the fluid above the hole.
First Scenario: Height h
- For a height h, the velocity of water exiting the hole is given by:
v = √(2gh).
- The volume of water is V = A0 * h (where A0 is the area of the tank).
- The time t to drain the water can be expressed as:
t = V / (A * v) = (A0 * h) / (A * √(2gh)).
- Simplifying gives us:
t = (A0√(h)) / (A√(2g)).
Second Scenario: Height 4h
- Now, if the height of water is increased to 4h, the velocity becomes:
v' = √(2g(4h)) = 2√(2gh).
- The new volume of water is:
V' = A0 * 4h.
- The new time t' to drain this water is:
t' = V' / (A * v') = (A0 * 4h) / (A * 2√(2gh)).
- This simplifies to:
t' = (2A0√(h)) / (A√(2g)).
Comparing Times
- From our expressions, we can see that:
t' = 4 * t / 2 = 2t.
- Hence, the correct answer for the time it takes to drain the water when the height is 4h is:
c) 2t seconds.
This illustrates that doubling the height of water leads to a different drainage time due to the relationship between height and velocity.
When water drains from a hole in a cylindrical vessel, the time it takes to drain is influenced by the height of the water and the area of the hole. We will use Torricelli's Law, which states that the speed of efflux of a fluid under gravity through an orifice is proportional to the square root of the height of the fluid above the hole.
First Scenario: Height h
- For a height h, the velocity of water exiting the hole is given by:
v = √(2gh).
- The volume of water is V = A0 * h (where A0 is the area of the tank).
- The time t to drain the water can be expressed as:
t = V / (A * v) = (A0 * h) / (A * √(2gh)).
- Simplifying gives us:
t = (A0√(h)) / (A√(2g)).
Second Scenario: Height 4h
- Now, if the height of water is increased to 4h, the velocity becomes:
v' = √(2g(4h)) = 2√(2gh).
- The new volume of water is:
V' = A0 * 4h.
- The new time t' to drain this water is:
t' = V' / (A * v') = (A0 * 4h) / (A * 2√(2gh)).
- This simplifies to:
t' = (2A0√(h)) / (A√(2g)).
Comparing Times
- From our expressions, we can see that:
t' = 4 * t / 2 = 2t.
- Hence, the correct answer for the time it takes to drain the water when the height is 4h is:
c) 2t seconds.
This illustrates that doubling the height of water leads to a different drainage time due to the relationship between height and velocity.
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Water is filled up to a height 'h' in a cylindrical vessel. Now, a hole of area 'A' is made at bottom of the vessel. Water drains out of the hole in time 't' seconds. If we repeat the above process with a height of water as '4h', then how much time it require for water to drain out of the cylinder?[Assume A << A0(area of tank)]a)t secondsb)4t secondsc)2t secondsd)t/4 secondsCorrect answer is option 'C'. Can you explain this answer?
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Water is filled up to a height 'h' in a cylindrical vessel. Now, a hole of area 'A' is made at bottom of the vessel. Water drains out of the hole in time 't' seconds. If we repeat the above process with a height of water as '4h', then how much time it require for water to drain out of the cylinder?[Assume A << A0(area of tank)]a)t secondsb)4t secondsc)2t secondsd)t/4 secondsCorrect answer is option 'C'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Water is filled up to a height 'h' in a cylindrical vessel. Now, a hole of area 'A' is made at bottom of the vessel. Water drains out of the hole in time 't' seconds. If we repeat the above process with a height of water as '4h', then how much time it require for water to drain out of the cylinder?[Assume A << A0(area of tank)]a)t secondsb)4t secondsc)2t secondsd)t/4 secondsCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Water is filled up to a height 'h' in a cylindrical vessel. Now, a hole of area 'A' is made at bottom of the vessel. Water drains out of the hole in time 't' seconds. If we repeat the above process with a height of water as '4h', then how much time it require for water to drain out of the cylinder?[Assume A << A0(area of tank)]a)t secondsb)4t secondsc)2t secondsd)t/4 secondsCorrect answer is option 'C'. Can you explain this answer?.
Water is filled up to a height 'h' in a cylindrical vessel. Now, a hole of area 'A' is made at bottom of the vessel. Water drains out of the hole in time 't' seconds. If we repeat the above process with a height of water as '4h', then how much time it require for water to drain out of the cylinder?[Assume A << A0(area of tank)]a)t secondsb)4t secondsc)2t secondsd)t/4 secondsCorrect answer is option 'C'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Water is filled up to a height 'h' in a cylindrical vessel. Now, a hole of area 'A' is made at bottom of the vessel. Water drains out of the hole in time 't' seconds. If we repeat the above process with a height of water as '4h', then how much time it require for water to drain out of the cylinder?[Assume A << A0(area of tank)]a)t secondsb)4t secondsc)2t secondsd)t/4 secondsCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Water is filled up to a height 'h' in a cylindrical vessel. Now, a hole of area 'A' is made at bottom of the vessel. Water drains out of the hole in time 't' seconds. If we repeat the above process with a height of water as '4h', then how much time it require for water to drain out of the cylinder?[Assume A << A0(area of tank)]a)t secondsb)4t secondsc)2t secondsd)t/4 secondsCorrect answer is option 'C'. Can you explain this answer?.
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