A bird is sitting in a large closed cage which is placed on a spring balance. It records a weight of 25 N. The bird (mass=0.5 kg) flies upward in the cage with an acceleration of `2m//s^(2)`. The spring balance will now record a weight of :-

Options

A. 24 N
B. 25 N
C. 26 N
D. 27 N

Answer

To solve the problem, we need to analyze the forces acting on the bird when it is flying upward in the cage.

### Step-by-Step Solution:

1. **Understand the Initial Condition:**
The spring balance initially records a weight of 25 N. This weight is the total weight of the cage and the bird combined.

2. **Calculate the Weight of the Bird:**
The weight of the bird can be calculated using the formula:
\[ W = mg \]
where \( m \) is the mass of the bird and \( g \) is the acceleration due to gravity (approximately \( 9.8 \, m/s^2 \)). Given that the mass of the bird is \( 0.5 \, kg \):
\[ W_{\text{bird}} = 0.5 \, kg \times 9.8 \, m/s^2 = 4.9 \, N \]

3. **Determine the Weight of the Cage:**
Since the total weight recorded by the spring balance is 25 N, we can find the weight of the cage by subtracting the weight of the bird:
\[ W_{\text{cage}} = 25 \, N - 4.9 \, N = 20.1 \, N \]

4. **Calculate the New Force When the Bird Flies Upward:**
When the bird flies upward with an acceleration of \( 2 \, m/s^2 \), we need to consider the forces acting on the bird. The effective force acting on the spring balance when the bird is flying upward is given by:
\[ F_{\text{new}} = W_{\text{bird}} + F_{\text{pseudo}} \]
where \( F_{\text{pseudo}} = ma \) (the pseudo force due to the bird's upward acceleration).

The pseudo force can be calculated as:
\[ F_{\text{pseudo}} = m \cdot a = 0.5 \, kg \cdot 2 \, m/s^2 = 1 \, N \]

5. **Calculate the Total Force on the Spring Balance:**
Now we can calculate the new reading on the spring balance:
\[ F_{\text{new}} = W_{\text{cage}} + (W_{\text{bird}} + F_{\text{pseudo}}) \]
Substituting the values:
\[ F_{\text{new}} = 20.1 \, N + (4.9 \, N + 1 \, N) = 20.1 \, N + 5.9 \, N = 26 \, N \]

6. **Final Answer:**
Therefore, the spring balance will now record a weight of **26 N**.