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The force required to row a boat at constant velocity is proportional to sqaure of it's speed. If a speed of vkm/hr requires 4kW, how much power does a speed of 2vkm/hr require? A) 8kW B) 16kW C) 24kW D) 32kW?
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Most Upvoted Answer
The force required to row a boat at constant velocity is proportional ...
Given, Force(F) is directly proportional to V^2...we know, power(P)=Work/time=F S/t..As power is directly proportional to F...,then Power is proportional to V^2...P2/P1=V2^2/V1^2..P2/4=(2V)^2/(V)^2....P2=16kW...
Community Answer
The force required to row a boat at constant velocity is proportional ...
Problem:
The force required to row a boat at a constant velocity is proportional to the square of its speed. If a speed of v km/hr requires 4 kW, how much power does a speed of 2v km/hr require?

Solution:
Given:
- The force required to row a boat at a constant velocity is proportional to the square of its speed.
- A speed of v km/hr requires 4 kW.

To Find:
- How much power does a speed of 2v km/hr require?

Let's Solve:

Step 1: Understand the Relationship
We are given that the force required to row a boat at a constant velocity is proportional to the square of its speed. This can be represented as:

Force ∝ Speed^2

Step 2: Use the Given Information
We are also given that a speed of v km/hr requires 4 kW. This means that when the boat is moving at a speed of v km/hr, the power required is 4 kW.

Step 3: Formulate the Equation
Let's assume that the power required for a speed of 2v km/hr is P. Since force is proportional to the square of speed, we can write:

P ∝ (2v)^2

Simplifying, we get:

P ∝ 4v^2

Step 4: Use the Proportionality Constant
Since we know that a speed of v km/hr requires 4 kW, we can use this information to find the proportionality constant. Let's substitute the values into the equation:

4 kW ∝ v^2

Step 5: Solve for the Proportionality Constant
To solve for the proportionality constant, we divide both sides of the equation by v^2:

4 kW / v^2 = constant

Step 6: Find the Power for 2v km/hr
Now that we have the proportionality constant, we can find the power required for a speed of 2v km/hr. Let's substitute the values into the equation:

P ∝ 4v^2

P = constant * (2v)^2

P = constant * 4v^2

Since the proportionality constant is the same, we can substitute it with 4 kW / v^2:

P = (4 kW / v^2) * 4v^2

P = 16 kW

Answer:
A speed of 2v km/hr requires 16 kW of power. Therefore, the correct answer is B) 16kW.
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Importance of high specific heat capacity of water for life Specific heat capacity of a substance is the amount of heat required to raise the temperature of that substance by 1 K. It is expressed in the units J/ (kg K). A high specific heat of a substance means that a large amount of heat is required to raise the temperature of the substance. Water has the highest known specific heat capacity. Its specific heat capacity is 4.186 K J/ (kg K) i.e. to raise the temperature of 1 kg of water by 1 Kelvin it requires 4.186 KJ of heat. For comparison sake, Copper requires only 385 Joules of heat to raise 1 kilogram of copper by 1 Kelvin. It also interesting to know that the specific heat capacities in two other phases of water (i.e. ice and water vapour) are less than this. High specific heat of water is mainly due to the presence of a large number of hydrogen bonds between molecules of water. On a beach on a sunny day, it is noticed that the sand is often quite hot to walk on, but the water is always cool, even in the shallows. This is because sand has a lower specific heat capacity than that of water. Sand takes less energy to raise the temperature by one degree. Because water has a high specific heat capacity, it requires more energy to raise the temperature by one degree. Since the sun puts same rate of energy on water and sand, which heats up sand more quickly and water more slowly. Water covers around 70% of the Earth's surface and its high specific heat plays a very important role to sustain life in the earth. It is able to absorb a lot of heat without a significant rise in the temperature. When temperatures decrease, the heat which is stored is released, restraining a rapid drop in temperature. The combined effect is the buffering of heat. A relatively constant temperature without sudden rise and drop is essential to sustain life. Hence water is important for life.Q. To raise the temperature of 1 kg of water and 1 kg of copper by 1 Kelvin, 4.186 KJ and 385 Joule of heat are required respectively. Which one will get heated up faster if exposed to sun?

Importance of high specific heat capacity of water for life Specific heat capacity of a substance is the amount of heat required to raise the temperature of that substance by 1 K. It is expressed in the units J/ (kg K). A high specific heat of a substance means that a large amount of heat is required to raise the temperature of the substance. Water has the highest known specific heat capacity. Its specific heat capacity is 4.186 K J/ (kg K) i.e. to raise the temperature of 1 kg of water by 1 Kelvin it requires 4.186 KJ of heat. For comparison sake, Copper requires only 385 Joules of heat to raise 1 kilogram of copper by 1 Kelvin. It also interesting to know that the specific heat capacities in two other phases of water (i.e. ice and water vapour) are less than this. High specific heat of water is mainly due to the presence of a large number of hydrogen bonds between molecules of water. On a beach on a sunny day, it is noticed that the sand is often quite hot to walk on, but the water is always cool, even in the shallows. This is because sand has a lower specific heat capacity than that of water. Sand takes less energy to raise the temperature by one degree. Because water has a high specific heat capacity, it requires more energy to raise the temperature by one degree. Since the sun puts same rate of energy on water and sand, which heats up sand more quickly and water more slowly. Water covers around 70% of the Earth's surface and its high specific heat plays a very important role to sustain life in the earth. It is able to absorb a lot of heat without a significant rise in the temperature. When temperatures decrease, the heat which is stored is released, restraining a rapid drop in temperature. The combined effect is the buffering of heat. A relatively constant temperature without sudden rise and drop is essential to sustain life. Hence water is important for life.Q. Which statement is false?

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Importance of high specific heat capacity of water for life Specific heat capacity of a substance is the amount of heat required to raise the temperature of that substance by 1 K. It is expressed in the units J/ (kg K). A high specific heat of a substance means that a large amount of heat is required to raise the temperature of the substance. Water has the highest known specific heat capacity. Its specific heat capacity is 4.186 K J/ (kg K) i.e. to raise the temperature of 1 kg of water by 1 Kelvin it requires 4.186 KJ of heat. For comparison sake, Copper requires only 385 Joules of heat to raise 1 kilogram of copper by 1 Kelvin. It also interesting to know that the specific heat capacities in two other phases of water (i.e. ice and water vapour) are less than this. High specific heat of water is mainly due to the presence of a large number of hydrogen bonds between molecules of water. On a beach on a sunny day, it is noticed that the sand is often quite hot to walk on, but the water is always cool, even in the shallows. This is because sand has a lower specific heat capacity than that of water. Sand takes less energy to raise the temperature by one degree. Because water has a high specific heat capacity, it requires more energy to raise the temperature by one degree. Since the sun puts same rate of energy on water and sand, which heats up sand more quickly and water more slowly. Water covers around 70% of the Earth's surface and its high specific heat plays a very important role to sustain life in the earth. It is able to absorb a lot of heat without a significant rise in the temperature. When temperatures decrease, the heat which is stored is released, restraining a rapid drop in temperature. The combined effect is the buffering of heat. A relatively constant temperature without sudden rise and drop is essential to sustain life. Hence water is important for life.Q. Specific heat capacity of ice is ............... than and specific heat capacity of water vapour is ............... than that of water.

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The force required to row a boat at constant velocity is proportional to sqaure of it's speed. If a speed of vkm/hr requires 4kW, how much power does a speed of 2vkm/hr require? A) 8kW B) 16kW C) 24kW D) 32kW?
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The force required to row a boat at constant velocity is proportional to sqaure of it's speed. If a speed of vkm/hr requires 4kW, how much power does a speed of 2vkm/hr require? A) 8kW B) 16kW C) 24kW D) 32kW? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about The force required to row a boat at constant velocity is proportional to sqaure of it's speed. If a speed of vkm/hr requires 4kW, how much power does a speed of 2vkm/hr require? A) 8kW B) 16kW C) 24kW D) 32kW? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The force required to row a boat at constant velocity is proportional to sqaure of it's speed. If a speed of vkm/hr requires 4kW, how much power does a speed of 2vkm/hr require? A) 8kW B) 16kW C) 24kW D) 32kW?.
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