STATEMENT-1:Work done by a force on a body can be added to kinetic energy of the body.
STATEMENT:2-By principle of homogeneity, any two physical quantities which are added must have same dimensions.

Options

A. Statement-1 is True , Statement-2 is True ,Statement-2 is a correct explanation for Statement-1
B. Statement-1 is True , Statement-2 is True ,Statement-2 is NOT a correct explanation for Statement-1
C. Statement-1 is True , Statement-2 is False
D. Statement-1 is False, Statement-2 is True

Answer

To solve the problem, we need to analyze both statements given in the question.

### Step 1: Understand Statement 1
**Statement 1:** Work done by a force on a body can be added to the kinetic energy of the body.

- Work done (W) is defined as the energy transferred when a force is applied to an object, causing it to move. The formula for work done is:
\[ W = F \cdot d \cdot \cos(\theta) \]
where \(F\) is the force, \(d\) is the displacement, and \(\theta\) is the angle between the force and the displacement direction.

- The unit of work done is Joules (J), which can also be expressed in terms of dimensions as \( [M^1 L^2 T^{-2}] \).

- Kinetic energy (KE) is the energy that an object possesses due to its motion, given by the formula:
\[ KE = \frac{1}{2} mv^2 \]
where \(m\) is the mass and \(v\) is the velocity.

- The unit of kinetic energy is also Joules (J), and its dimensions are the same as that of work done: \( [M^1 L^2 T^{-2}] \).

### Conclusion for Step 1:
Since both work done and kinetic energy have the same dimensions and units, they can indeed be added together. Therefore, **Statement 1 is true**.

### Step 2: Understand Statement 2
**Statement 2:** By the principle of homogeneity, any two physical quantities which are added must have the same dimensions.

- The principle of homogeneity states that in any physical equation, all terms must have the same dimensions. This is essential for the mathematical validity of the equation.

- For example, if we were to add work done (in Joules) to kinetic energy (also in Joules), both quantities must have the same dimensions, which they do.

### Conclusion for Step 2:
Since the principle of homogeneity is correctly stated and applies to the addition of work done and kinetic energy, **Statement 2 is also true**.

### Final Conclusion:
Both statements are true, and Statement 2 correctly explains Statement 1. Therefore, the answer is that both statements are true, and Statement 2 is a correct explanation of Statement 1.