A body of mass `1.0` kg is falling with an acceleration of 10 `m//s^(2)` . Its apparent weight will be `(g=10m//sec^(2))`

Options

A. `1.0` kg wt
B. `2.0` kg wt
C. `0.5` kg wt
D. Zero

Answer

To determine the apparent weight of a body of mass 1.0 kg falling with an acceleration of 10 m/s², we can follow these steps:

### Step 1: Understand the Forces Acting on the Body
The body is falling under the influence of gravity. The force due to gravity (weight) acting on the body can be calculated using the formula:
\[ W = mg \]
where:
- \( m = 1.0 \, \text{kg} \) (mass of the body)
- \( g = 10 \, \text{m/s}^2 \) (acceleration due to gravity)

### Step 2: Calculate the Weight of the Body
Substituting the values into the weight formula:
\[ W = 1.0 \, \text{kg} \times 10 \, \text{m/s}^2 = 10 \, \text{N} \]
So, the weight of the body is 10 N.

### Step 3: Determine the Apparent Weight
When the body is in free fall, it accelerates downwards at the same rate as gravity. The apparent weight is the normal force acting on the body. In free fall, the normal force is zero because the body is not in contact with any surface that would exert an upward force.

Using the equation for apparent weight:
\[ N = W - ma \]
where:
- \( N \) = apparent weight (normal force)
- \( W \) = weight of the body
- \( a \) = acceleration of the body (which is equal to \( g \) in this case)

Since the body is falling with an acceleration equal to \( g \):
\[ N = mg - mg = 0 \]

### Conclusion
The apparent weight of the body is 0 N, indicating that the body is in a state of free fall and experiences weightlessness.

### Final Answer
The apparent weight of the body is **0 N**.

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