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Which of the following is not a vector?...

Which of the following is not a vector?

A

Angular momentum

B

Angular impulse

C

Kinetic energy

D

Magnetic Intensity

Text Solution

AI Generated Solution

The correct Answer is:
To determine which of the following options is not a vector, we need to analyze each option provided. ### Step-by-Step Solution: 1. **Identify the Options**: We have four options to consider: - Option 1: Angular Momentum - Option 2: Angular Impulse - Option 3: Kinetic Energy - Option 4: Magnetic Intensity 2. **Analyze Option 1: Angular Momentum**: - Angular momentum (L) is defined as the cross product of the position vector (R) and linear momentum vector (P): \[ L = R \times P \] - Since it is derived from the cross product of two vectors, angular momentum is a vector quantity. **Hint**: Remember that the cross product of two vectors results in another vector. 3. **Analyze Option 2: Angular Impulse**: - Angular impulse is defined as torque (τ) multiplied by a time interval (dt): \[ \text{Angular Impulse} = \tau \cdot dt \] - Torque (τ) is also a vector quantity, and since time (dt) is a scalar, the product of a vector and a scalar remains a vector. Thus, angular impulse is a vector. **Hint**: The product of a vector and a scalar is still a vector. 4. **Analyze Option 3: Kinetic Energy**: - Kinetic energy (KE) is defined as: \[ KE = \frac{1}{2} mv^2 \] - Here, m is mass (a scalar) and v is velocity (a vector). However, when calculating kinetic energy, we square the velocity, which makes it a scalar quantity. Therefore, kinetic energy is not a vector. **Hint**: Energy is a scalar quantity, regardless of the vector nature of velocity in its formula. 5. **Analyze Option 4: Magnetic Intensity**: - Magnetic intensity is related to the magnetic moment (a vector) divided by volume (a scalar): \[ \text{Magnetic Intensity} = \frac{M}{V} \] - Since the magnetic moment is a vector and volume is a scalar, the resultant magnetic intensity remains a vector. **Hint**: Division of a vector by a scalar retains the vector nature. 6. **Conclusion**: - After analyzing all options, we find that: - Angular Momentum (Option 1) is a vector. - Angular Impulse (Option 2) is a vector. - Kinetic Energy (Option 3) is **not a vector**. - Magnetic Intensity (Option 4) is a vector. - Therefore, the correct answer is **Option 3: Kinetic Energy**. ### Final Answer: **Kinetic Energy is not a vector.**

To determine which of the following options is not a vector, we need to analyze each option provided. ### Step-by-Step Solution: 1. **Identify the Options**: We have four options to consider: - Option 1: Angular Momentum - Option 2: Angular Impulse - Option 3: Kinetic Energy ...
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