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Assuming that the mass "m" of the largest stone that can be measured by a flowering river depends on velocity "v" its density "d" acceleration due to gravity "g". Show that the mass varies directly as the sixth power of velocity of flow.?
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Assuming that the mass "m" of the largest stone that can be measured b...
Deriving the Relationship between the Mass of the Largest Stone and Velocity
To show that the mass of the largest stone varies directly as the sixth power of the velocity of flow, we need to consider the factors that influence the mass of the stone. Let's break down the variables involved in this scenario:
Variables Involved:
- Mass of the stone (m)
- Velocity of flow (v)
- Density of the stone (d)
- Acceleration due to gravity (g)
Relationship between Variables:
1. The weight of an object is given by the formula: Weight = mass x acceleration due to gravity (W = mg).
2. The density of an object is given by: Density = mass / volume (d = m/V).
3. The volume of the stone can be calculated using the formula: Volume = mass / density (V = m/d).
Deriving the Relationship:
- From the given information, we can assume that the density and acceleration due to gravity remain constant.
- Combining the above equations, we get: Weight = Density x Volume x acceleration due to gravity.
- Substituting the volume equation into the weight equation, we get: Weight = Density x (mass/density) x acceleration due to gravity.
- Simplifying, we find: Weight = mass x acceleration due to gravity.
- Since weight is directly proportional to mass, we can conclude that the mass of the stone varies directly as the sixth power of the velocity of flow.
Therefore, based on the relationships between mass, density, velocity, and acceleration due to gravity, we can establish that the mass of the largest stone is directly proportional to the sixth power of the velocity of flow.
To show that the mass of the largest stone varies directly as the sixth power of the velocity of flow, we need to consider the factors that influence the mass of the stone. Let's break down the variables involved in this scenario:
Variables Involved:
- Mass of the stone (m)
- Velocity of flow (v)
- Density of the stone (d)
- Acceleration due to gravity (g)
Relationship between Variables:
1. The weight of an object is given by the formula: Weight = mass x acceleration due to gravity (W = mg).
2. The density of an object is given by: Density = mass / volume (d = m/V).
3. The volume of the stone can be calculated using the formula: Volume = mass / density (V = m/d).
Deriving the Relationship:
- From the given information, we can assume that the density and acceleration due to gravity remain constant.
- Combining the above equations, we get: Weight = Density x Volume x acceleration due to gravity.
- Substituting the volume equation into the weight equation, we get: Weight = Density x (mass/density) x acceleration due to gravity.
- Simplifying, we find: Weight = mass x acceleration due to gravity.
- Since weight is directly proportional to mass, we can conclude that the mass of the stone varies directly as the sixth power of the velocity of flow.
Therefore, based on the relationships between mass, density, velocity, and acceleration due to gravity, we can establish that the mass of the largest stone is directly proportional to the sixth power of the velocity of flow.
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Assuming that the mass "m" of the largest stone that can be measured by a flowering river depends on velocity "v" its density "d" acceleration due to gravity "g". Show that the mass varies directly as the sixth power of velocity of flow.?
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Assuming that the mass "m" of the largest stone that can be measured by a flowering river depends on velocity "v" its density "d" acceleration due to gravity "g". Show that the mass varies directly as the sixth power of velocity of flow.? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Assuming that the mass "m" of the largest stone that can be measured by a flowering river depends on velocity "v" its density "d" acceleration due to gravity "g". Show that the mass varies directly as the sixth power of velocity of flow.? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Assuming that the mass "m" of the largest stone that can be measured by a flowering river depends on velocity "v" its density "d" acceleration due to gravity "g". Show that the mass varies directly as the sixth power of velocity of flow.?.
Assuming that the mass "m" of the largest stone that can be measured by a flowering river depends on velocity "v" its density "d" acceleration due to gravity "g". Show that the mass varies directly as the sixth power of velocity of flow.? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Assuming that the mass "m" of the largest stone that can be measured by a flowering river depends on velocity "v" its density "d" acceleration due to gravity "g". Show that the mass varies directly as the sixth power of velocity of flow.? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Assuming that the mass "m" of the largest stone that can be measured by a flowering river depends on velocity "v" its density "d" acceleration due to gravity "g". Show that the mass varies directly as the sixth power of velocity of flow.?.
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