(A) : When a lift moves with uniform velocity the man in the lift will feel weightlessness.
(R) : In downward motion of a lift, apparent weight of a body in it decreases.

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 false but ( R) is true
D. Both (A) and (R ) are false

Answer

To solve the question, we need to analyze both the assertion (A) and the reason (R) provided.

### Step 1: Analyze the Assertion (A)
The assertion states: "When a lift moves with uniform velocity, the man in the lift will feel weightlessness."

- When a lift moves with uniform velocity, it means that the lift has a constant speed and is not accelerating.
- In this scenario, the forces acting on a person inside the lift are balanced. The gravitational force (weight) acting downwards is equal to the normal force acting upwards.
- Therefore, the person does not experience any sensation of weightlessness; they feel their normal weight (mg).

**Conclusion**: The assertion (A) is **false**.

### Step 2: Analyze the Reason (R)
The reason states: "In the downward motion of a lift, the apparent weight of a body in it decreases."

- When a lift is moving downwards with acceleration (let's say 'a'), the forces acting on a person inside the lift are:
- Gravitational force (weight) acting downwards: \( mg \)
- Normal force (apparent weight) acting upwards: \( N \)
- According to Newton's second law, if the lift is accelerating downwards, the net force acting on the person can be expressed as:
\[ mg - N = ma \]
- Rearranging this gives:
\[ N = mg - ma \]
- This shows that the apparent weight \( N \) decreases as the lift accelerates downwards, because \( N \) is less than \( mg \).

**Conclusion**: The reason (R) is **true**.

### Final Conclusion
- Assertion (A) is false.
- Reason (R) is true.

Thus, the correct answer is: **A is false but R is true.**