Assertion: An object of mass `m_1` and another of mass `m_2(m_2gtm_1)` are released from certain distance. The objects move towards each other under the gravitational force between them. In this motion, centre of mass of their system will continuously move towards the heavier mass `m_2`.
Reason: In a system of a heavier and a lighter mass, centre of mass lies closer to the heavier mass.

Options

A. (a) If both Assertion and Reason are true and the Reason is correct explanation of the Assertion.
B. (b) If both Assertion and Reason are true but Reason is not the correct explanation of Assertion.
C. (c) If Assertion is true, but the Reason is false.
D. (d) If Assertion is false but the Reason is true.

Explanation

To solve the question, we need to analyze both the assertion and the reason provided.

### Step 1: Understand the Assertion
The assertion states that when two objects of mass \( m_1 \) (lighter mass) and \( m_2 \) (heavier mass) are released from a certain distance, they will move towards each other due to gravitational attraction, and the center of mass of the system will continuously move towards the heavier mass \( m_2 \).

### Step 2: Analyze the Motion of the Center of Mass
The center of mass (COM) of a two-body system can be calculated using the formula:
\[ x_{cm} = \frac{m_1 x_1 + m_2 x_2}{m_1 + m_2} \]
where \( x_1 \) and \( x_2 \) are the positions of masses \( m_1 \) and \( m_2 \) respectively.

As both masses move towards each other, the forces acting on them due to gravity are internal forces. According to the law of conservation of momentum, the center of mass of a closed system remains constant if only internal forces are acting.

### Step 3: Conclusion on the Assertion
Since the center of mass does not move due to internal forces, the assertion that the center of mass will continuously move towards the heavier mass \( m_2 \) is **incorrect**.

### Step 4: Understand the Reason
The reason states that in a system of a heavier and a lighter mass, the center of mass lies closer to the heavier mass. This is a true statement. The position of the center of mass is influenced by the relative magnitudes of the masses.

### Step 5: Conclusion on the Reason
The reason is **true** because the center of mass will always be closer to the heavier mass \( m_2 \) when \( m_2 > m_1 \).

### Final Conclusion
- The assertion is **false**.
- The reason is **true**.

Thus, the correct option is that the assertion is false and the reason is true.