Can a body possess K.E. without having momentum?

Answer

To determine whether a body can possess kinetic energy (K.E.) without having momentum, let's analyze the definitions and relationships between kinetic energy and momentum.

### Step-by-Step Solution:

1. **Understanding Kinetic Energy**:
- Kinetic energy (K.E.) is defined as the energy that an object possesses due to its motion. The formula for kinetic energy is given by:
\[ K.E. = \frac{1}{2} mv^2 \]
where \( m \) is the mass of the object and \( v \) is its velocity.

2. **Understanding Momentum**:
- Momentum (p) is defined as the product of an object's mass and its velocity. The formula for momentum is:
\[ p = mv \]

3. **Analyzing the Conditions**:
- For an object to have kinetic energy, it must be in motion, which means its velocity \( v \) must be greater than zero. If the velocity is zero, then:
\[ K.E. = \frac{1}{2} m(0)^2 = 0 \]
- Similarly, if the velocity is zero, the momentum will also be:
\[ p = m(0) = 0 \]

4. **Conclusion**:
- Since both kinetic energy and momentum depend on the velocity of the object, if an object has kinetic energy, it must have a non-zero velocity, which implies it also has momentum. Therefore, a body cannot possess kinetic energy without having momentum.

### Final Answer:
No, a body cannot possess kinetic energy without having momentum.

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