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The scalar quantity among the following ...

The scalar quantity among the following is

A

weight of body

B

temperature gradient

C

TENSION

D

ELECTRIC POTENTINAL

Text Solution

AI Generated Solution

The correct Answer is:
To determine the scalar quantity among the given options, we need to understand what scalar quantities are and analyze each option accordingly. ### Step-by-Step Solution: 1. **Understanding Scalar Quantities**: - Scalar quantities are defined as those that have only magnitude and no direction. Examples include temperature, mass, speed, and electric potential. 2. **Analyzing the Options**: - **Option 1: Weight of the body**: - Weight is the force exerted by gravity on an object and is calculated as \( W = mg \) (mass times acceleration due to gravity). Since weight has both magnitude and direction (it acts downwards), it is a vector quantity. - **Conclusion**: Incorrect. - **Option 2: Temperature Gradient**: - The temperature gradient is defined as the rate of change of temperature with respect to distance, expressed mathematically as \( \frac{dT}{dx} \). This quantity has a direction (it indicates the direction of increasing temperature) and thus is also a vector quantity. - **Conclusion**: Incorrect. - **Option 3: Tension**: - Tension is a force that is transmitted through a string, rope, or wire when it is pulled tight by forces acting from opposite ends. Like weight, tension has both magnitude and direction, making it a vector quantity. - **Conclusion**: Incorrect. - **Option 4: Electric Potential**: - Electric potential is defined as the amount of electric potential energy per unit charge at a point in space. It is a scalar quantity because it has only magnitude and no direction. The formula for electric potential due to a point charge is given by \( V = \frac{kq}{r} \), where \( k \) is a constant, \( q \) is the charge, and \( r \) is the distance from the charge. - **Conclusion**: Correct. 3. **Final Answer**: - The scalar quantity among the options provided is **Electric Potential**.

To determine the scalar quantity among the given options, we need to understand what scalar quantities are and analyze each option accordingly. ### Step-by-Step Solution: 1. **Understanding Scalar Quantities**: - Scalar quantities are defined as those that have only magnitude and no direction. Examples include temperature, mass, speed, and electric potential. 2. **Analyzing the Options**: ...
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