(A) : Two particles (starting from rest) move towards each other under a mutual force of attraction. The velocity of their c.m is zero.
(R ) : Internal forces do not alter the state of motion of c.m.

Options

A. Both (A) and (R ) are true and (R ) is the correct explanation of (A)
B. Both (A) and (R ) are true and (R ) is not the correct explanation of (A)
C. (A) is true but (R ) is false
D. Both (A) and (R ) are false

Answer

To solve the problem, we need to analyze the assertion (A) and the reason (R) given in the question.

### Step-by-Step Solution:

1. **Understanding the Assertion (A)**:
- The assertion states that two particles start from rest and move towards each other due to a mutual force of attraction, and that the velocity of their center of mass (c.m) is zero.
- Since both particles are initially at rest and only move towards each other due to their mutual attraction, we can conclude that the center of mass of the system remains stationary.

2. **Analyzing the Center of Mass**:
- The center of mass (c.m) of a system of particles is defined as the point where the total mass of the system can be considered to be concentrated for the purpose of analyzing motion.
- The formula for the center of mass (R) of two particles (m1 and m2) located at positions (x1 and x2) is given by:
\[ R = \frac{m_1 x_1 + m_2 x_2}{m_1 + m_2} \]
- If both particles start from rest and move towards each other, the center of mass will remain at the same position if there are no external forces acting on the system.

3. **Understanding the Reason (R)**:
- The reason states that internal forces do not alter the state of motion of the center of mass.
- This is a fundamental principle in mechanics. Internal forces (forces between the particles) can change the velocities of the individual particles, but they do not affect the overall motion of the center of mass of the system.

4. **Conclusion**:
- Both the assertion (A) and the reason (R) are true.
- The reason (R) correctly explains the assertion (A) because the center of mass remains stationary due to the absence of external forces, even though the particles are moving towards each other due to their mutual attraction.

### Final Answer:
Both the assertion and the reason are true, and the reason is the correct explanation for the assertion.