Which of the following statements is false :

Options

A. Mass, speed and energy are scalars
B. Momentum, force and torque are vectors
C. Distance is a scalar while displacement is a vector
D. A vector has only magnitude whereas as a scalar has both magnitude and direction

Answer

To determine which statement is false among the given options, we will analyze each statement one by one.

### Step-by-Step Solution:

1. **Statement A: Mass, speed, energy are scalars.**
- **Analysis:** Scalars are quantities that have only magnitude and no direction. Mass, speed, and energy fit this definition as they are described solely by their size (magnitude).
- **Conclusion:** This statement is **true**.

2. **Statement B: Momentum, force, and torque are vectors.**
- **Analysis:** Vectors are quantities that have both magnitude and direction.
- Momentum is defined as the product of mass and velocity (which is a vector), hence momentum is a vector.
- Force is defined as mass times acceleration (where acceleration is also a vector), thus force is a vector.
- Torque is defined as the cross product of force and distance (both of which are vectors), making torque a vector as well.
- **Conclusion:** This statement is **true**.

3. **Statement C: Distance is a scalar while displacement is a vector.**
- **Analysis:** Distance measures the total path length traveled and has only magnitude, making it a scalar. Displacement measures the change in position and has both magnitude and direction, making it a vector.
- **Conclusion:** This statement is **true**.

4. **Statement D: A vector has only magnitude whereas a scalar has both magnitude and direction.**
- **Analysis:** This statement contradicts the definitions of vectors and scalars. A vector indeed has both magnitude and direction, while a scalar has only magnitude.
- **Conclusion:** This statement is **false**.

### Final Answer:
The false statement is **Statement D**: "A vector has only magnitude whereas a scalar has both magnitude and direction."

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