A lift is moving up with an acceleration of 3.675 `m//sec_(2)`. The weight of a man-

Options

A. increases by `36.75%`
B. decreases by `37.5%`
C. increases by `137.5%`
D. remains the same

Answer

To solve the problem, we need to determine how the weight experienced by a man in a lift moving upwards with an acceleration of 3.675 m/s² changes, compared to his weight when the lift is at rest.

### Step-by-step Solution:

1. **Identify the Forces Acting on the Man:**
- When the lift is accelerating upwards, the forces acting on the man include:
- The gravitational force (weight) acting downwards: \( W = mg \)
- The normal force (apparent weight) acting upwards: \( N \)

2. **Apply Newton's Second Law:**
- According to Newton's second law, the net force acting on the man in the upward direction can be expressed as:
\[ N - mg = ma \]
- Here, \( a \) is the upward acceleration of the lift.

3. **Rearranging the Equation:**
- Rearranging the equation gives us the normal force:
\[ N = mg + ma \]
- This shows that the normal force (apparent weight) is greater than the gravitational force when the lift is accelerating upwards.

4. **Substituting Values:**
- We can express the normal force in terms of the man's weight:
\[ N = mg + ma = mg + m(3.675) \]
- Factoring out \( m \):
\[ N = m(g + a) = m(g + 3.675) \]

5. **Calculating the Percentage Increase in Weight:**
- The percentage increase in weight can be calculated using the formula:
\[ \text{Percentage Increase} = \frac{N - mg}{mg} \times 100\% \]
- Substituting for \( N \):
\[ \text{Percentage Increase} = \frac{m(g + 3.675) - mg}{mg} \times 100\% \]
- Simplifying:
\[ \text{Percentage Increase} = \frac{m \cdot 3.675}{mg} \times 100\% \]
- Canceling \( m \):
\[ \text{Percentage Increase} = \frac{3.675}{g} \times 100\% \]

6. **Using \( g = 9.8 \, \text{m/s}^2 \):**
- Now, substituting \( g \):
\[ \text{Percentage Increase} = \frac{3.675}{9.8} \times 100\% \]
- Calculating this gives:
\[ \text{Percentage Increase} \approx 37.5\% \]

### Final Answer:
The weight of the man is increased by **37.5%** when the lift is moving upwards with an acceleration of 3.675 m/s².