The work done by all the forces (external and internal) on a system equals the change in

Options

A. (a)total energy
B. (b)kinetic energy
C. (c)potential energy
D. (d)none of these

Answer

To solve the question, we need to apply the work-energy theorem, which relates the work done by all forces acting on a system to the change in kinetic energy of that system.

### Step-by-Step Solution:

1. **Understanding the Work-Energy Theorem**:
The work-energy theorem states that the total work done by all forces (both external and internal) on a system is equal to the change in kinetic energy of that system.

\[ W = \Delta KE \]

2. **Defining Work Done (W)**:
Work done on a system can be expressed as the difference between the final kinetic energy and the initial kinetic energy.

\[ W = KE_{final} - KE_{initial} \]

3. **Kinetic Energy Formula**:
The kinetic energy (KE) of an object is given by the formula:

\[ KE = \frac{1}{2} mv^2 \]

where \(m\) is the mass of the object and \(v\) is its velocity.

4. **Expressing Change in Kinetic Energy**:
The change in kinetic energy (\(\Delta KE\)) can be expressed as:

\[ \Delta KE = KE_{final} - KE_{initial} = \frac{1}{2} mv_{final}^2 - \frac{1}{2} mv_{initial}^2 \]

5. **Conclusion**:
According to the work-energy theorem, the work done by all forces on a system equals the change in kinetic energy. Therefore, the correct answer to the question is:

**B. Kinetic Energy**