A man of mass 60 kg records his weight on a weighing machine placed inside a lift . The ratio of the weights of the man recorded when the lift is ascending up with a uniform speed of 2 m/s to when it is descending down with a uniform speed of 4 m/s will be

Options

A. a) 2
B. b) 1
C. c) 0.5
D. d) None of these

Explanation

To solve the problem, we need to analyze the situation when the man is in the lift both ascending and descending at constant speeds.

### Step-by-Step Solution:

1. **Understanding Weight Measurement**:
The weight measured by the weighing machine (apparent weight) is affected by the acceleration of the lift. The apparent weight is given by the formula:
\[ W' = m(g + a) \]
where \( W' \) is the apparent weight, \( m \) is the mass of the man, \( g \) is the acceleration due to gravity (approximately \( 9.81 \, \text{m/s}^2 \)), and \( a \) is the acceleration of the lift.

2. **Lift Ascending at Constant Speed**:
When the lift is ascending at a constant speed of \( 2 \, \text{m/s} \), the acceleration \( a = 0 \) (since the speed is constant). Therefore, the apparent weight \( W_{up} \) is:
\[ W_{up} = m \cdot g = 60 \, \text{kg} \cdot 9.81 \, \text{m/s}^2 = 588.6 \, \text{N} \]

3. **Lift Descending at Constant Speed**:
Similarly, when the lift is descending at a constant speed of \( 4 \, \text{m/s} \), the acceleration \( a = 0 \) as well. Thus, the apparent weight \( W_{down} \) is:
\[ W_{down} = m \cdot g = 60 \, \text{kg} \cdot 9.81 \, \text{m/s}^2 = 588.6 \, \text{N} \]

4. **Calculating the Ratio of Weights**:
Now, we can find the ratio of the weights recorded when the lift is ascending to when it is descending:
\[ \text{Ratio} = \frac{W_{up}}{W_{down}} = \frac{588.6 \, \text{N}}{588.6 \, \text{N}} = 1 \]

5. **Conclusion**:
Therefore, the ratio of the weights of the man recorded when the lift is ascending to when it is descending is:
\[ \text{Ratio} = 1 \]

### Final Answer:
The correct option is **1**.