The apparent weight of the body, when it is travelling upwards with an acceleration of `2m//s^(2)` and mass is 10 kg , will be

Options

A. 198 N
B. 164 N
C. 140 N
D. 118 N

Answer

To find the apparent weight of a body traveling upwards with an acceleration of \(2 \, \text{m/s}^2\) and having a mass of \(10 \, \text{kg}\), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the forces acting on the body**:
- The weight of the body (\(W\)) acting downwards is given by:
\[ W = mg \]
- The normal force (\(N\)) acting upwards is what we are trying to find, which represents the apparent weight.

2. **Calculate the weight of the body**:
- Given that the mass \(m = 10 \, \text{kg}\) and taking \(g \approx 10 \, \text{m/s}^2\) for simplicity:
\[ W = mg = 10 \, \text{kg} \times 10 \, \text{m/s}^2 = 100 \, \text{N} \]

3. **Apply Newton's second law**:
- When the body is accelerating upwards, the net force acting on it can be expressed as:
\[ N - W = ma \]
- Here, \(a = 2 \, \text{m/s}^2\) is the upward acceleration.

4. **Substitute the known values into the equation**:
- Rearranging the equation gives:
\[ N = W + ma \]
- Now substituting \(W = 100 \, \text{N}\) and \(ma = 10 \, \text{kg} \times 2 \, \text{m/s}^2 = 20 \, \text{N}\):
\[ N = 100 \, \text{N} + 20 \, \text{N} = 120 \, \text{N} \]

5. **Conclusion**:
- The apparent weight of the body when it is traveling upwards with an acceleration of \(2 \, \text{m/s}^2\) is:
\[ N = 120 \, \text{N} \]