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Can you explain the answer of this question below:
Magnitude of force F experienced by a certain object moving with speed v is given by F = Kv3, where K is a constant. The dimensions of K are
- A:[M-2LT]
- B:[ML-3T]
- C:[MLT-2]
- D:[ML-2T]
The answer is d.
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Can you explain the answer of this question below:Magnitude of force F...
Dimensions of Force and Velocity
The dimensions of a physical quantity are a way to represent its nature and units. In this question, we are given that the magnitude of force experienced by an object is given by F = Kv^3, where K is a constant. To determine the dimensions of K, we need to analyze the dimensions of force (F) and velocity (v) separately.
The dimensions of force (F) can be expressed as [M L T^-2], where:
- [M] represents the dimension of mass,
- [L] represents the dimension of length, and
- [T^-2] represents the dimension of time raised to the power of -2 (indicating acceleration).
The dimensions of velocity (v) can be expressed as [L T^-1], where:
- [L] represents the dimension of length, and
- [T^-1] represents the dimension of time raised to the power of -1 (indicating rate of change of position).
Dimensions of the Constant K
To determine the dimensions of the constant K, we can rearrange the equation F = Kv^3 as follows:
F = K(v^3)
K = F/(v^3)
Substituting the dimensions of force and velocity, we have:
[M L T^-2] = [K]([L T^-1]^3)
[M L T^-2] = [K]([L^3 T^-3])
[M L T^-2] = [K L^3 T^-3]
Comparing the dimensions on both sides of the equation, we can determine the dimensions of the constant K.
The dimensions of K are [M L^-2 T^3], which can be simplified to [M L^-2 T].
Therefore, the correct answer is option D: [ML^-2T].
The dimensions of a physical quantity are a way to represent its nature and units. In this question, we are given that the magnitude of force experienced by an object is given by F = Kv^3, where K is a constant. To determine the dimensions of K, we need to analyze the dimensions of force (F) and velocity (v) separately.
The dimensions of force (F) can be expressed as [M L T^-2], where:
- [M] represents the dimension of mass,
- [L] represents the dimension of length, and
- [T^-2] represents the dimension of time raised to the power of -2 (indicating acceleration).
The dimensions of velocity (v) can be expressed as [L T^-1], where:
- [L] represents the dimension of length, and
- [T^-1] represents the dimension of time raised to the power of -1 (indicating rate of change of position).
Dimensions of the Constant K
To determine the dimensions of the constant K, we can rearrange the equation F = Kv^3 as follows:
F = K(v^3)
K = F/(v^3)
Substituting the dimensions of force and velocity, we have:
[M L T^-2] = [K]([L T^-1]^3)
[M L T^-2] = [K]([L^3 T^-3])
[M L T^-2] = [K L^3 T^-3]
Comparing the dimensions on both sides of the equation, we can determine the dimensions of the constant K.
The dimensions of K are [M L^-2 T^3], which can be simplified to [M L^-2 T].
Therefore, the correct answer is option D: [ML^-2T].
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Can you explain the answer of this question below:Magnitude of force F experienced by a certain object moving with speed v is given by F = Kv3, where K is a constant. The dimensions of K areA:[M-2LT]B:[ML-3T]C:[MLT-2]D:[ML-2T]The answer is d. for Class 11 2025 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about Can you explain the answer of this question below:Magnitude of force F experienced by a certain object moving with speed v is given by F = Kv3, where K is a constant. The dimensions of K areA:[M-2LT]B:[ML-3T]C:[MLT-2]D:[ML-2T]The answer is d. covers all topics & solutions for Class 11 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Can you explain the answer of this question below:Magnitude of force F experienced by a certain object moving with speed v is given by F = Kv3, where K is a constant. The dimensions of K areA:[M-2LT]B:[ML-3T]C:[MLT-2]D:[ML-2T]The answer is d..
Can you explain the answer of this question below:Magnitude of force F experienced by a certain object moving with speed v is given by F = Kv3, where K is a constant. The dimensions of K areA:[M-2LT]B:[ML-3T]C:[MLT-2]D:[ML-2T]The answer is d. for Class 11 2025 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about Can you explain the answer of this question below:Magnitude of force F experienced by a certain object moving with speed v is given by F = Kv3, where K is a constant. The dimensions of K areA:[M-2LT]B:[ML-3T]C:[MLT-2]D:[ML-2T]The answer is d. covers all topics & solutions for Class 11 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Can you explain the answer of this question below:Magnitude of force F experienced by a certain object moving with speed v is given by F = Kv3, where K is a constant. The dimensions of K areA:[M-2LT]B:[ML-3T]C:[MLT-2]D:[ML-2T]The answer is d..
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