A person of mass m is on the floor of a lift. The lift is moving down with an acceleration 'a'. Then :
a) the net force is acting in downward direction and is equal to mg
b) the force mg must be greater than reaction force
c) the man appears to be lighter than his true weight by a factor (a/g)

Options

A. a, b, c are correct
B. b and c are correct
C. a and c are correct
D. only b is correct

Answer

To solve the problem, we need to analyze the forces acting on a person of mass \( m \) inside a lift that is accelerating downwards with an acceleration \( a \).

### Step-by-Step Solution:

1. **Identify Forces Acting on the Person**:
- The weight of the person acting downwards: \( F_g = mg \) (where \( g \) is the acceleration due to gravity).
- The normal reaction force \( N \) acting upwards from the floor of the lift.

2. **Consider the Acceleration of the Lift**:
- Since the lift is accelerating downwards with an acceleration \( a \), we can apply Newton's second law to the person in the lift.

3. **Apply Newton's Second Law**:
- The net force acting on the person can be expressed as:
\[ F_{\text{net}} = F_g - N = ma \]
- Here, \( F_g \) (downwards) is greater than \( N \) (upwards) because the lift is accelerating downwards.

4. **Rearranging the Equation**:
- We can rearrange the equation to find the normal force:
\[ mg - N = ma \implies N = mg - ma \]
- This shows that the normal force \( N \) is less than the gravitational force \( mg \).

5. **Determine the Relationship Between Forces**:
- From the equation \( N = mg - ma \), we can see that:
\[ N = m(g - a) \]
- This indicates that the normal force \( N \) is less than the gravitational force \( mg \), confirming that \( mg > N \).

6. **Apparent Weight**:
- The apparent weight \( W_a \) of the person is given by the normal force \( N \):
\[ W_a = N = mg - ma \]
- To find the factor by which the man appears lighter, we can express the apparent weight in terms of the true weight:
\[ W_a = mg - ma = m(g - a) \]
- The factor by which the man appears lighter compared to his true weight \( mg \) is:
\[ \text{Factor} = \frac{W_a}{mg} = \frac{m(g - a)}{mg} = 1 - \frac{a}{g} \]

### Conclusion:
- **Statement A**: The net force is acting in the downward direction and is equal to \( mg \) - **False**.
- **Statement B**: The force \( mg \) must be greater than the reaction force - **True**.
- **Statement C**: The man appears to be lighter than his true weight by a factor \( \frac{a}{g} \) - **True**.

Thus, the correct options are **B and C**.