The kinetic energy of a body is increased most by doubling its

Options

A. mass
B. density
C. weight
D. speed

Answer

To solve the question regarding how the kinetic energy of a body is increased most by doubling its mass, density, weight, or speed, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Formula for Kinetic Energy**:
The formula for kinetic energy (KE) is given by:
\[ KE = \frac{1}{2} mv^2 \]
where \( m \) is the mass of the body and \( v \) is its velocity (speed).

2. **Analyze the Options**:
We have four options to consider:
- Option 1: Mass
- Option 2: Density
- Option 3: Weight
- Option 4: Speed

3. **Evaluate the Impact of Doubling Each Option**:
- **Doubling Mass**: If we double the mass (\( m \to 2m \)):
\[ KE' = \frac{1}{2} (2m) v^2 = m v^2 \]
The new kinetic energy is twice the original kinetic energy.

- **Doubling Density**: Density does not directly affect kinetic energy, so this option can be disregarded.

- **Doubling Weight**: Weight is related to mass (Weight = mass × gravity). Doubling weight implies doubling mass, which we already evaluated. Thus, this option is also disregarded.

- **Doubling Speed**: If we double the speed (\( v \to 2v \)):
\[ KE' = \frac{1}{2} m (2v)^2 = \frac{1}{2} m (4v^2) = 2mv^2 \]
The new kinetic energy becomes four times the original kinetic energy.

4. **Compare the Increases**:
- Doubling mass results in a 2x increase in kinetic energy.
- Doubling speed results in a 4x increase in kinetic energy.

5. **Conclusion**:
Since doubling the speed results in a greater increase in kinetic energy compared to doubling the mass, the correct answer is:
\[ \text{The kinetic energy of a body is increased most by doubling its speed.} \]

### Final Answer:
The kinetic energy of a body is increased most by doubling its **speed** (Option 4).

---