A light spring balance hangs from the hook of the other light spring balance and a block of mass M kg hangs from the former one. Then the true statement about the scale reading is

Options

A. both the scales read M kg each
B. the scale of the lower one reads M kg and of the upper one zero
C. the reading of the two scales can be anything but the sum of the reading will be M kg
D. both the scales read `M //2` kg

Answer

To solve the problem regarding the readings of two light spring balances, we will analyze the forces acting on the system step by step.

### Step-by-Step Solution:

1. **Understanding the Setup**:
- We have two light spring balances. The lower spring balance (let's call it Spring 2) has a block of mass \( M \) hanging from it. The upper spring balance (Spring 1) is hanging from the ceiling and supports Spring 2.

2. **Identifying Forces**:
- The block of mass \( M \) exerts a downward force due to gravity, which is \( F = Mg \), where \( g \) is the acceleration due to gravity.
- This force \( Mg \) will cause an extension in Spring 2.

3. **Reading of the Lower Spring Balance (Spring 2)**:
- The reading on Spring 2 will be equal to the weight of the block hanging from it. Therefore, the reading of Spring 2 is:
\[ \text{Reading of Spring 2} = Mg \]

4. **Analyzing the Upper Spring Balance (Spring 1)**:
- Spring 1 supports the entire system, including Spring 2 and the block. The force acting on Spring 1 is the weight of the block \( Mg \) plus the force due to the extension of Spring 2.
- Since Spring 2 is in equilibrium, the force exerted by Spring 2 (which is equal to \( Mg \)) is balanced by the force exerted by Spring 1.

5. **Reading of the Upper Spring Balance (Spring 1)**:
- The reading on Spring 1 will be equal to the total weight it supports, which is just the weight of the block \( Mg \) since Spring 2 is also in equilibrium.
- Thus, the reading of Spring 1 is:
\[ \text{Reading of Spring 1} = Mg \]

6. **Conclusion**:
- Both spring balances read the same value, which is \( Mg \). Therefore, the true statement about the scale readings is that both scales read \( Mg \).

### Final Answer:
Both spring balances read \( Mg \).

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