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Physics · SYSTEMS OF PARTICLES AND ROTATIONAL MOTION
हिन्दीMatch List-I with List-II: List-I (Physical Quantity) List-II (Defining Vector Relation) A Linear velocity in rotation I \( \frac{d\vec{\omega}}{dt} \) B Torque (Moment of force) II \( \vec{\omega} \times \vec{r} \) C Newton's second law for system III \( \vec{r} \times \vec{F} \) D Angular acceleration vector IV \( \frac{d\vec{P}}{dt} = \vec{F}_{\text{ext}} \) Choose the correct answer from the options given below:
Match List-I with List-II:
| List-I (Physical Quantity) | List-II (Defining Vector Relation) | ||
|---|---|---|---|
| A | Linear velocity in rotation | I | \( \frac{d\vec{\omega}}{dt} \) |
| B | Torque (Moment of force) | II | \( \vec{\omega} \times \vec{r} \) |
| C | Newton's second law for system | III | \( \vec{r} \times \vec{F} \) |
| D | Angular acceleration vector | IV | \( \frac{d\vec{P}}{dt} = \vec{F}_{\text{ext}} \) |
Choose the correct answer from the options given below:
Correct answer · Option 4
A-(II), B-(III), C-(IV), D-(I)
Explanation
Linear velocity is \( \vec{v} = \vec{\omega} \times \vec{r} \) (A-II). Torque is \( \vec{\tau} = \vec{r} \times \vec{F} \) (B-III). System momentum derivative gives net external force \( \frac{d\vec{P}}{dt} = \vec{F}_{\text{ext}} \) (C-IV). Angular acceleration is \( \vec{\alpha} = \frac{d\vec{\omega}}{dt} \) (D-I).
