Which one of the following quantities is a scalar ?

Options

A. Volume
B. Torque
C. Force
D. Acceleration

Answer

To determine which of the following quantities is a scalar, we need to understand the definition of scalar and vector quantities.

**Step 1: Understand Scalar and Vector Quantities**
- A scalar quantity is defined as a quantity that has only magnitude and no direction. Examples include mass, temperature, and volume.
- A vector quantity, on the other hand, has both magnitude and direction. Examples include force, velocity, and torque.

**Step 2: Analyze the Options**
- We need to evaluate each option provided to identify which one is a scalar.

**Option 1: Volume**
- Volume measures the amount of space an object occupies. It is expressed in cubic units (e.g., liters, cubic meters) and does not have a direction. Therefore, volume is a scalar quantity.

**Option 2: Torque**
- Torque is defined as the rotational equivalent of linear force and is calculated using the formula \( \tau = R \times F \) (where \( R \) is the distance vector and \( F \) is the force vector). Since torque involves a cross product of two vectors, it has both magnitude and direction, making it a vector quantity.

**Option 3: Force**
- Force is defined as mass times acceleration (\( F = m \cdot a \)). Since acceleration is a vector (it has both magnitude and direction), force is also a vector quantity.

**Option 4: (not specified in the transcript)**
- Without the fourth option specified, we cannot analyze it. However, we already have enough information from the first three options.

**Step 3: Conclusion**
- Based on the analysis, the only quantity that is a scalar is **Volume**.

**Final Answer: Volume is a scalar quantity.**

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