A man of mass 70 kg stands on a weighing scale in a lift which is moving downward with the uniform acceleration of `5 m/s^2` . The reading on the weighing scale is

Options

A. 70 kg
B. 35 kg
C. 105 kg
D. 700 kg

Answer

To solve the problem, we need to determine the reading on the weighing scale when a man of mass 70 kg is in a lift that is moving downward with a uniform acceleration of \(5 \, \text{m/s}^2\).

### Step-by-Step Solution:

1. **Identify the forces acting on the man:**
- The weight of the man acting downward is given by the formula:
\[ W = m \cdot g \]
where \(m = 70 \, \text{kg}\) and \(g = 10 \, \text{m/s}^2\) (approximating gravitational acceleration).
- Therefore, the weight \(W\) is:
\[ W = 70 \, \text{kg} \cdot 10 \, \text{m/s}^2 = 700 \, \text{N} \]

2. **Determine the pseudo force acting on the man:**
- Since the lift is accelerating downward, a pseudo force acts upward on the man. This pseudo force \(F_{\text{pseudo}}\) can be calculated using:
\[ F_{\text{pseudo}} = m \cdot a \]
where \(a = 5 \, \text{m/s}^2\) (the downward acceleration of the lift).
- Thus, the pseudo force is:
\[ F_{\text{pseudo}} = 70 \, \text{kg} \cdot 5 \, \text{m/s}^2 = 350 \, \text{N} \]

3. **Calculate the net force acting on the weighing scale:**
- The net force \(F_{\text{net}}\) exerted on the weighing scale is the difference between the weight of the man and the pseudo force:
\[ F_{\text{net}} = W - F_{\text{pseudo}} = 700 \, \text{N} - 350 \, \text{N} = 350 \, \text{N} \]

4. **Determine the reading on the weighing scale:**
- The reading on the weighing scale corresponds to the apparent weight of the man, which can be calculated by dividing the net force by \(g\):
\[ \text{Reading} = \frac{F_{\text{net}}}{g} = \frac{350 \, \text{N}}{10 \, \text{m/s}^2} = 35 \, \text{kg} \]

### Final Answer:
The reading on the weighing scale is **35 kg**.