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A model boat, 1/100 size of its prototype has 0.12 N of resistance when simulating a speed of 5 m/s of the prototype. Water is the fluid in both cases. What is the corresponding resistance in the prototype?
[The frictional forces can be neglected]
[The frictional forces can be neglected]
- a)1.2 kN
- b)12 kN
- c)120 kN
- d)1.2 mN
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
A model boat, 1/100 size of its prototype has 0.12 N of resistance whe...
The resistance offered at the free surface is the significant force and as such Froude model law is appropriate
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Most Upvoted Answer
A model boat, 1/100 size of its prototype has 0.12 N of resistance whe...
Given:
- Model boat is 1/100 size of its prototype.
- Model boat has a resistance of 0.12 N when simulating a speed of 5 m/s of the prototype.
- Both the model boat and the prototype are in water.
To find:
The corresponding resistance in the prototype.
Solution:
Step 1: Understanding the Scale
The model boat is 1/100 size of its prototype. This means that all the dimensions of the model boat are 1/100 of the dimensions of the prototype. However, the resistance is not directly proportional to the size. We need to consider the scale effects.
Step 2: Understanding the Resistance
Resistance is the force that opposes the motion of an object through a fluid. In this case, the fluid is water. The resistance experienced by an object depends on factors such as the shape of the object, the velocity of the object, and the properties of the fluid.
Step 3: Understanding the Relationship between Resistance and Scale
When the size of an object changes, the resistance experienced by the object does not change linearly. In fluid dynamics, the resistance experienced by an object is proportional to the square of its characteristic dimension (length, width, or height). Therefore, if the size of an object is reduced by a factor of 1/n, the resistance experienced by the object will be reduced by a factor of 1/n^2.
Step 4: Calculating the Corresponding Resistance
In this case, the model boat is 1/100 size of the prototype. Therefore, the resistance experienced by the model boat is 1/(100^2) = 1/10000 times the resistance experienced by the prototype.
Given that the resistance of the model boat is 0.12 N, we can calculate the resistance of the prototype as follows:
Resistance of prototype = Resistance of model boat * (1/10000)
Resistance of prototype = 0.12 N * (1/10000)
Resistance of prototype = 0.12 N * 0.0001
Resistance of prototype = 0.000012 N
Converting 0.000012 N to millinewtons (mN):
Resistance of prototype = 0.000012 N * 1000
Resistance of prototype = 0.012 mN
Therefore, the corresponding resistance in the prototype is 0.012 mN, which is equivalent to option C.
- Model boat is 1/100 size of its prototype.
- Model boat has a resistance of 0.12 N when simulating a speed of 5 m/s of the prototype.
- Both the model boat and the prototype are in water.
To find:
The corresponding resistance in the prototype.
Solution:
Step 1: Understanding the Scale
The model boat is 1/100 size of its prototype. This means that all the dimensions of the model boat are 1/100 of the dimensions of the prototype. However, the resistance is not directly proportional to the size. We need to consider the scale effects.
Step 2: Understanding the Resistance
Resistance is the force that opposes the motion of an object through a fluid. In this case, the fluid is water. The resistance experienced by an object depends on factors such as the shape of the object, the velocity of the object, and the properties of the fluid.
Step 3: Understanding the Relationship between Resistance and Scale
When the size of an object changes, the resistance experienced by the object does not change linearly. In fluid dynamics, the resistance experienced by an object is proportional to the square of its characteristic dimension (length, width, or height). Therefore, if the size of an object is reduced by a factor of 1/n, the resistance experienced by the object will be reduced by a factor of 1/n^2.
Step 4: Calculating the Corresponding Resistance
In this case, the model boat is 1/100 size of the prototype. Therefore, the resistance experienced by the model boat is 1/(100^2) = 1/10000 times the resistance experienced by the prototype.
Given that the resistance of the model boat is 0.12 N, we can calculate the resistance of the prototype as follows:
Resistance of prototype = Resistance of model boat * (1/10000)
Resistance of prototype = 0.12 N * (1/10000)
Resistance of prototype = 0.12 N * 0.0001
Resistance of prototype = 0.000012 N
Converting 0.000012 N to millinewtons (mN):
Resistance of prototype = 0.000012 N * 1000
Resistance of prototype = 0.012 mN
Therefore, the corresponding resistance in the prototype is 0.012 mN, which is equivalent to option C.
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A model boat, 1/100 size of its prototype has 0.12 N of resistance when simulating a speed of 5 m/s of the prototype. Water is the fluid in both cases. What is the corresponding resistance in the prototype?[The frictional forces can be neglected]a)1.2 kNb)12 kNc)120 kNd)1.2 mNCorrect answer is option 'C'. Can you explain this answer?
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A model boat, 1/100 size of its prototype has 0.12 N of resistance when simulating a speed of 5 m/s of the prototype. Water is the fluid in both cases. What is the corresponding resistance in the prototype?[The frictional forces can be neglected]a)1.2 kNb)12 kNc)120 kNd)1.2 mNCorrect answer is option 'C'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A model boat, 1/100 size of its prototype has 0.12 N of resistance when simulating a speed of 5 m/s of the prototype. Water is the fluid in both cases. What is the corresponding resistance in the prototype?[The frictional forces can be neglected]a)1.2 kNb)12 kNc)120 kNd)1.2 mNCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A model boat, 1/100 size of its prototype has 0.12 N of resistance when simulating a speed of 5 m/s of the prototype. Water is the fluid in both cases. What is the corresponding resistance in the prototype?[The frictional forces can be neglected]a)1.2 kNb)12 kNc)120 kNd)1.2 mNCorrect answer is option 'C'. Can you explain this answer?.
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