A block tied between identical springs is in equilibrium. If upper spring is cut, then the acceleration of the block just after cut is `5 ms^(1)` Now if instead of upper string lower spring is cut, then the acceleration of the block just after the cut will be (Take `g=10 m//s^(2)`).

Options

A. `1.25 ms^(-2)`
B. `5 ms^(-2)`
C. `10 ms^(-2)`
D. `2.5 ms^(-2)`

Explanation

To solve the problem, we need to analyze the forces acting on the block when one of the springs is cut. Let's break it down step by step.

### Step-by-Step Solution:

1. **Understanding the Setup**:
- We have a block of mass \( m \) suspended between two identical springs.
- The weight of the block \( mg \) acts downwards, where \( g = 10 \, \text{m/s}^2 \).
- The forces exerted by the springs are \( F_1 \) (upper spring) and \( F_2 \) (lower spring).

2. **Equilibrium Condition**:
- In equilibrium, the forces acting on the block must balance out. Thus, we have:
\[ F_1 + F_2 = mg \quad \text{(Equation 1)} \]

3. **Cutting the Upper Spring**:
- When the upper spring \( F_1 \) is cut, the only forces acting on the block are its weight \( mg \) downwards and the force \( F_2 \) from the lower spring upwards.
- The net force acting on the block can be expressed as:
\[ mg - F_2 = ma \quad \text{(where \( a = 5 \, \text{m/s}^2 \))} \]
- Substituting \( g = 10 \, \text{m/s}^2 \):
\[ 10m - F_2 = 5m \]
- Rearranging gives:
\[ F_2 = 10m - 5m = 5m \quad \text{(Equation 2)} \]

4. **Finding \( F_1 \)**:
- Now, substituting \( F_2 \) back into Equation 1:
\[ F_1 + 5m = 10m \]
- Thus, we find:
\[ F_1 = 10m - 5m = 5m \quad \text{(Equation 3)} \]

5. **Cutting the Lower Spring**:
- Now, consider the scenario where the lower spring \( F_2 \) is cut.
- The forces acting on the block are its weight \( mg \) downwards and the force \( F_1 \) from the upper spring upwards.
- The net force can be expressed as:
\[ mg - F_1 = ma' \quad \text{(where \( a' \) is the new acceleration)} \]
- Substituting \( g = 10 \, \text{m/s}^2 \) and \( F_1 = 5m \):
\[ 10m - 5m = ma' \]
- This simplifies to:
\[ 5m = ma' \]
- Dividing both sides by \( m \) (assuming \( m \neq 0 \)):
\[ a' = 5 \, \text{m/s}^2 \]

### Final Answer:
The acceleration of the block just after cutting the lower spring is \( 5 \, \text{m/s}^2 \).