A man of mass m is on the floor of a lift. The lift moving up with acceleration 'a', then :
a) the net unbalanced force on him is 'ma'
b) the normal reaction exerted by the floor on the man is m(g + a)
c) the apparent weight is greater than his true weight

Options

A. a, b, c are correct
B. a, b, c are wrong
C. a & c are correct
D. b & c are correct

Answer

To solve the problem, let's analyze the situation step by step.

### Step 1: Identify the forces acting on the man
When the lift is accelerating upwards with an acceleration 'a', two main forces act on the man:
- The gravitational force (weight) acting downwards, which is \( mg \).
- The normal force (reaction force) exerted by the floor of the lift acting upwards, which we will denote as \( N \).

### Step 2: Apply Newton's second law
According to Newton's second law, the net force acting on the man can be expressed as:
\[ F_{\text{net}} = ma \]
In this case, the net force is the difference between the normal force and the weight of the man:
\[ F_{\text{net}} = N - mg \]
Setting these two expressions equal gives us:
\[ N - mg = ma \]

### Step 3: Solve for the normal force \( N \)
Rearranging the equation from Step 2 to solve for \( N \):
\[ N = mg + ma \]
This can be factored as:
\[ N = m(g + a) \]

### Step 4: Determine the apparent weight
The apparent weight of the man is defined as the normal force \( N \) acting on him. From Step 3, we found that:
\[ N = m(g + a) \]
Thus, the apparent weight is greater than the true weight (which is \( mg \)) because:
\[ N = mg + ma > mg \]
This indicates that the apparent weight is indeed greater than the true weight when the lift is accelerating upwards.

### Conclusion
Based on our analysis:
- The net unbalanced force on him is \( ma \) (this is true since \( F_{\text{net}} = ma \)).
- The normal reaction exerted by the floor on the man is \( m(g + a) \) (this is derived from our calculations).
- The apparent weight is greater than his true weight (as shown in our conclusion).

Thus, all statements (a, b, and c) are correct.