The apparent weight of a body , weighing M kg wt , during free fall is

Options

A. less than M kg wt
B. more than M kg wt
C. equal to M kg wt
D. zero

Answer

To determine the apparent weight of a body weighing \( M \) kg during free fall, we can follow these steps:

### Step 1: Understand the Concept of Weight
The weight of a body is given by the formula:
\[ W = m \cdot g \]
where \( m \) is the mass of the body and \( g \) is the acceleration due to gravity (approximately \( 9.81 \, \text{m/s}^2 \) on the surface of the Earth).

### Step 2: Define Free Fall
When an object is in free fall, it is accelerating downwards at the same rate as gravity. This means that the only force acting on the object is gravity itself.

### Step 3: Analyze the Situation in Free Fall
In free fall, the body experiences gravitational force \( F_g \) downwards, which is equal to \( m \cdot g \). However, if we consider an elevator or any frame of reference that is also in free fall, we need to account for the effects of this non-inertial frame.

### Step 4: Consider the Pseudo Force
In a non-inertial frame (like a free-falling elevator), a pseudo force acts on the body in the opposite direction of the acceleration. Since the elevator is falling downwards with acceleration \( g \), the pseudo force acts upwards with a magnitude of \( m \cdot g \).

### Step 5: Calculate the Apparent Weight
The apparent weight \( W_a \) is defined as the normal force acting on the body. In free fall, the gravitational force \( F_g \) and the pseudo force \( F_p \) cancel each other out:
\[ W_a = F_g - F_p \]
Substituting the values:
\[ W_a = (m \cdot g) - (m \cdot g) = 0 \]

### Conclusion
Thus, the apparent weight of the body during free fall is:
\[ \text{Apparent Weight} = 0 \]