Assertion `:-` Two objects of equal mass rest on the opposite pan of an arm balance. Scale will remains balanced, when it is accelerated up or down in a lift.
Reason `:-` Both masses experience equal fictitious forces magnitude as well as direction.

Options

A. If both Assertion & Reason are True & the Reason is a correct explanation of the Assertion.
B. If both Assertion & Reason are True but Reason is not a correct explanation of the Assertiion.
C. If Assertion is True but the Reason is False.
D. If both Assertion & Reason are False

Explanation

To solve the question regarding the assertion and reason about the balance of two objects in a lift, we can break it down step by step.

### Step-by-Step Solution:

1. **Understanding the System**:
We have two objects of equal mass resting on opposite pans of an arm balance. When the lift accelerates, we need to analyze how this affects the balance.

**Hint**: Identify the forces acting on the masses when the system is at rest and when the lift is accelerating.

2. **Forces Acting on the Masses**:
When the lift is stationary, the only force acting on each mass is its weight (mg), where m is the mass and g is the acceleration due to gravity. Since both masses are equal, the forces are equal, and the scale is balanced.

**Hint**: Consider what happens to the forces when the lift accelerates.

3. **Effect of Lift Acceleration**:
When the lift accelerates upwards with acceleration 'a', the effective gravitational force acting on each mass becomes (g + a). Conversely, if the lift accelerates downwards, the effective gravitational force becomes (g - a).

**Hint**: Use the concept of effective gravity to analyze the situation.

4. **Calculating the Effective Force**:
- For upward acceleration:
\[ F_{\text{effective}} = m(g + a) \]
- For downward acceleration:
\[ F_{\text{effective}} = m(g - a) \]

**Hint**: Remember that both masses are equal, so their effective forces will be equal regardless of the direction of acceleration.

5. **Net Torque Calculation**:
The torque about the pivot point remains zero because both masses are equal and experience the same effective force. Thus, the balance is maintained.

**Hint**: Think about how torque is calculated and how equal forces at equal distances from the pivot affect balance.

6. **Conclusion**:
Since both masses experience equal effective forces (either both (g + a) or both (g - a)), the scale remains balanced regardless of whether the lift is accelerating upwards or downwards. Therefore, both the assertion and reason are true.

### Final Statement:
Both the assertion that the scale remains balanced during acceleration and the reason that both masses experience equal fictitious forces in magnitude and direction are correct.

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