A spring balance is attached to the ceiling of a lift. A man hangs his bag on the spring and the spring reads 49N, when the lift is stationary. If the lift moves downward with an acceleration of `5m//2^2`, the reading of the spring balance will be

Options

A. (a) 24N
B. (b) 74N
C. (c) 15N
D. (d) 49N

Explanation

To solve the problem, we need to determine the reading of the spring balance when the lift is moving downwards with an acceleration of \(5 \, \text{m/s}^2\).

### Step-by-Step Solution:

1. **Identify the Forces:**
- When the lift is stationary, the spring balance reads the weight of the bag, which is \(W = 49 \, \text{N}\).
- The weight of the bag can be expressed as \(W = mg\), where \(m\) is the mass of the bag and \(g\) is the acceleration due to gravity (\(g \approx 9.8 \, \text{m/s}^2\)).

2. **Calculate the Mass of the Bag:**
- We can find the mass \(m\) of the bag using the equation:
\[ W = mg \implies m = \frac{W}{g} = \frac{49 \, \text{N}}{9.8 \, \text{m/s}^2} \approx 5 \, \text{kg} \]

3. **Apply Newton's Second Law:**
- When the lift is accelerating downwards, the net force acting on the bag can be described by Newton's second law:
\[ F_{\text{net}} = ma \]
- The forces acting on the bag are the weight \(W\) acting downwards and the tension \(T\) in the spring acting upwards. The equation can be written as:
\[ W - T = ma \]
- Here, \(a\) is the acceleration of the lift, which is \(5 \, \text{m/s}^2\).

4. **Substitute the Known Values:**
- We know \(W = 49 \, \text{N}\), \(m = 5 \, \text{kg}\), and \(a = 5 \, \text{m/s}^2\). Plugging these values into the equation gives:
\[ 49 \, \text{N} - T = 5 \, \text{kg} \times 5 \, \text{m/s}^2 \]
\[ 49 \, \text{N} - T = 25 \, \text{N} \]

5. **Solve for Tension \(T\):**
- Rearranging the equation to solve for \(T\):
\[ T = 49 \, \text{N} - 25 \, \text{N} = 24 \, \text{N} \]

6. **Conclusion:**
- The reading of the spring balance when the lift is moving downwards with an acceleration of \(5 \, \text{m/s}^2\) will be \(T = 24 \, \text{N}\).

### Final Answer:
The reading of the spring balance will be **24 N**.