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Kinetic energy of a particle moving along elliptical trajectory is given by k=alpha S^2, where s is the distance travelled by the particle the dimensions of alpha are?
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Kinetic energy of a particle moving along elliptical trajectory is giv...
Understanding Kinetic Energy Expression
The kinetic energy \( k \) of a particle moving along an elliptical trajectory is expressed as \( k = \alpha S^2 \), where \( S \) is the distance traveled by the particle.
Breaking Down the Equation
- Kinetic Energy (k): The dimensions of kinetic energy are derived from the formula \( k = \frac{1}{2} mv^2 \).
- Dimensions: \([M^1 L^2 T^{-2}]\)
- Distance Traveled (S): This is simply a measure of length.
- Dimensions: \([L^1]\)
Analyzing Dimensions of \( \alpha \)
To find the dimensions of the constant \( \alpha \), we rearrange the equation:
\[ \alpha = \frac{k}{S^2} \]
Substituting the dimensions we have:
- Dimensions of \( k \): \([M^1 L^2 T^{-2}]\)
- Dimensions of \( S^2 \): \([L^1]^2 = [L^2]\)
Now, substituting these into the rearranged equation:
\[ \alpha = \frac{[M^1 L^2 T^{-2}]}{[L^2]} \]
This simplifies to:
\[ \alpha = [M^1 T^{-2}] \]
Final Dimensions of \( \alpha \)
- The dimensions of \( \alpha \) are \([M^1 T^{-2}]\).
This indicates that \( \alpha \) represents a physical quantity that relates mass and time squared, which is essential in the context of kinetic energy in motion along a trajectory.
The kinetic energy \( k \) of a particle moving along an elliptical trajectory is expressed as \( k = \alpha S^2 \), where \( S \) is the distance traveled by the particle.
Breaking Down the Equation
- Kinetic Energy (k): The dimensions of kinetic energy are derived from the formula \( k = \frac{1}{2} mv^2 \).
- Dimensions: \([M^1 L^2 T^{-2}]\)
- Distance Traveled (S): This is simply a measure of length.
- Dimensions: \([L^1]\)
Analyzing Dimensions of \( \alpha \)
To find the dimensions of the constant \( \alpha \), we rearrange the equation:
\[ \alpha = \frac{k}{S^2} \]
Substituting the dimensions we have:
- Dimensions of \( k \): \([M^1 L^2 T^{-2}]\)
- Dimensions of \( S^2 \): \([L^1]^2 = [L^2]\)
Now, substituting these into the rearranged equation:
\[ \alpha = \frac{[M^1 L^2 T^{-2}]}{[L^2]} \]
This simplifies to:
\[ \alpha = [M^1 T^{-2}] \]
Final Dimensions of \( \alpha \)
- The dimensions of \( \alpha \) are \([M^1 T^{-2}]\).
This indicates that \( \alpha \) represents a physical quantity that relates mass and time squared, which is essential in the context of kinetic energy in motion along a trajectory.
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Kinetic energy of a particle moving along elliptical trajectory is given by k=alpha S^2, where s is the distance travelled by the particle the dimensions of alpha are?
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Kinetic energy of a particle moving along elliptical trajectory is given by k=alpha S^2, where s is the distance travelled by the particle the dimensions of alpha are? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about Kinetic energy of a particle moving along elliptical trajectory is given by k=alpha S^2, where s is the distance travelled by the particle the dimensions of alpha are? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Kinetic energy of a particle moving along elliptical trajectory is given by k=alpha S^2, where s is the distance travelled by the particle the dimensions of alpha are?.
Kinetic energy of a particle moving along elliptical trajectory is given by k=alpha S^2, where s is the distance travelled by the particle the dimensions of alpha are? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about Kinetic energy of a particle moving along elliptical trajectory is given by k=alpha S^2, where s is the distance travelled by the particle the dimensions of alpha are? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Kinetic energy of a particle moving along elliptical trajectory is given by k=alpha S^2, where s is the distance travelled by the particle the dimensions of alpha are?.
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