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In a certain system, there are only two fundamental quantities - force and time. If their dimensions are [F] and [T] respectively, what are the dimensions of linear momentum in this system?
- a)[F1T3]
- b)[F1T1]
- c)[F-1T2]
- d)[F2T2]
Correct answer is option 'B'. Can you explain this answer?
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In a certain system, there are only two fundamental quantities - force...
Dimensions of Linear Momentum:
Linear momentum is defined as the product of mass and velocity. In the given system, only force and time are considered as fundamental quantities. Therefore, we need to express mass and velocity in terms of force and time to determine the dimensions of linear momentum.
Expressing Mass in terms of Force and Time:
Since force is a fundamental quantity, it can be expressed in terms of mass, acceleration, and time using Newton's second law of motion:
Force = mass × acceleration
Rearranging the equation, we get:
Mass = Force / acceleration
Acceleration has dimensions of [L/T^2] (where [L] represents length), so we can rewrite the equation as:
Mass = Force / [L/T^2]
We can simplify the equation further by multiplying the numerator and denominator by T^2:
Mass = (Force × T^2) / L
The dimension of mass in this system is [F1T2/L].
Expressing Velocity in terms of Force and Time:
Velocity is defined as the rate of change of displacement with respect to time. Displacement has dimensions of [L], and time has dimensions of [T]. Therefore, velocity can be expressed as:
Velocity = Displacement / Time
Dividing both the numerator and denominator of the equation by T, we get:
Velocity = (Displacement / T) / 1
Since displacement divided by time represents average velocity, we can rewrite the equation as:
Velocity = (Displacement / T) × (1 / 1)
The dimension of velocity in this system is [L/T].
Calculating the Dimensions of Linear Momentum:
Linear momentum is the product of mass and velocity. Substituting the dimensions of mass and velocity that we derived earlier, we get:
Linear Momentum = (Mass) × (Velocity)
= [F1T2/L] × [L/T]
= [F1T1]
Therefore, the dimensions of linear momentum in this system are [F1T1], which corresponds to option B.
Linear momentum is defined as the product of mass and velocity. In the given system, only force and time are considered as fundamental quantities. Therefore, we need to express mass and velocity in terms of force and time to determine the dimensions of linear momentum.
Expressing Mass in terms of Force and Time:
Since force is a fundamental quantity, it can be expressed in terms of mass, acceleration, and time using Newton's second law of motion:
Force = mass × acceleration
Rearranging the equation, we get:
Mass = Force / acceleration
Acceleration has dimensions of [L/T^2] (where [L] represents length), so we can rewrite the equation as:
Mass = Force / [L/T^2]
We can simplify the equation further by multiplying the numerator and denominator by T^2:
Mass = (Force × T^2) / L
The dimension of mass in this system is [F1T2/L].
Expressing Velocity in terms of Force and Time:
Velocity is defined as the rate of change of displacement with respect to time. Displacement has dimensions of [L], and time has dimensions of [T]. Therefore, velocity can be expressed as:
Velocity = Displacement / Time
Dividing both the numerator and denominator of the equation by T, we get:
Velocity = (Displacement / T) / 1
Since displacement divided by time represents average velocity, we can rewrite the equation as:
Velocity = (Displacement / T) × (1 / 1)
The dimension of velocity in this system is [L/T].
Calculating the Dimensions of Linear Momentum:
Linear momentum is the product of mass and velocity. Substituting the dimensions of mass and velocity that we derived earlier, we get:
Linear Momentum = (Mass) × (Velocity)
= [F1T2/L] × [L/T]
= [F1T1]
Therefore, the dimensions of linear momentum in this system are [F1T1], which corresponds to option B.
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In a certain system, there are only two fundamental quantities - force and time. If their dimensions are [F] and [T] respectively, what are the dimensions of linear momentum in this system?a)[F1T3]b)[F1T1]c)[F-1T2]d)[F2T2]Correct answer is option 'B'. Can you explain this answer? for NEET 2025 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about In a certain system, there are only two fundamental quantities - force and time. If their dimensions are [F] and [T] respectively, what are the dimensions of linear momentum in this system?a)[F1T3]b)[F1T1]c)[F-1T2]d)[F2T2]Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for NEET 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a certain system, there are only two fundamental quantities - force and time. If their dimensions are [F] and [T] respectively, what are the dimensions of linear momentum in this system?a)[F1T3]b)[F1T1]c)[F-1T2]d)[F2T2]Correct answer is option 'B'. Can you explain this answer?.
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