A man of mass 60 kg records his wt. on a weighing machine placed inside a lift. The ratio of wts. Of man recorded when 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. `0.5`
B. 1
C. 2
D. none of these

Explanation

To solve the problem, we need to analyze the weight recorded by the weighing machine in two different scenarios: when the lift is ascending with a uniform speed and when it is descending with a uniform speed.

### Step-by-Step Solution:

1. **Understanding Weight in a Lift**:
- The weight (W) of an object is given by the formula:
\[ W = mg \]
where \( m \) is the mass of the object and \( g \) is the acceleration due to gravity (approximately \( 9.8 \, \text{m/s}^2 \)).
- In a lift, the reading on the weighing machine (apparent weight) can change depending on the lift's motion.

2. **Weight When Lift is Ascending**:
- When the lift ascends with a uniform speed, there is no net acceleration acting on the man. Therefore, the apparent weight remains the same as his actual weight.
- The weight recorded by the machine when the lift is ascending:
\[ W_{\text{up}} = mg = 60 \, \text{kg} \times 9.8 \, \text{m/s}^2 = 588 \, \text{N} \]

3. **Weight When Lift is Descending**:
- When the lift descends with a uniform speed, again there is no net acceleration acting on the man. The apparent weight remains the same as his actual weight.
- The weight recorded by the machine when the lift is descending:
\[ W_{\text{down}} = mg = 60 \, \text{kg} \times 9.8 \, \text{m/s}^2 = 588 \, \text{N} \]

4. **Calculating the Ratio of Weights**:
- The ratio of the weights recorded when the lift is ascending to when it is descending is:
\[ \text{Ratio} = \frac{W_{\text{up}}}{W_{\text{down}}} = \frac{588 \, \text{N}}{588 \, \text{N}} = 1 \]

### Final Answer:
The ratio of weights recorded when the lift is ascending with a uniform speed of 2 m/s to when it is descending with a uniform speed of 4 m/s is **1**.

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