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A light spring balance hangs from the ho...

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

A

(a)Both the scales read M/2 kilogram each

B

(b)Both the scales read M kilogram each

C

(c)The scale of the lower one reads M kilogram and of the upper one zero

D

(d)The reading of the two scales can be anything but the sum of the reading will be M kilogram

Text Solution

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The correct Answer is:
To solve the problem, we need to analyze the setup of the two spring balances and the block of mass \( M \) kg hanging from them. ### Step-by-Step Solution: 1. **Understanding the Setup**: - We have two light spring balances. The first spring balance (let's call it Balance A) is hanging from a hook. The second spring balance (Balance B) is hanging from Balance A. - A block of mass \( M \) kg is hanging from Balance B. 2. **Drawing the Diagram**: - Draw a vertical line representing the hook. - Below the hook, draw Balance A. - Below Balance A, draw Balance B. - Finally, below Balance B, draw the block of mass \( M \) kg. 3. **Analyzing Forces**: - The block of mass \( M \) exerts a downward force due to gravity, which is \( F = M \cdot g \), where \( g \) is the acceleration due to gravity. - Since Balance B is directly supporting the block, it will read the weight of the block, which is \( M \cdot g \). 4. **Reading of Balance B**: - Balance B will show a reading of \( M \cdot g \) because it is measuring the weight of the block. 5. **Reading of Balance A**: - Balance A supports Balance B and the block. Therefore, the force it experiences is the sum of the forces from Balance B and the weight of the block. - Since Balance B reads \( M \cdot g \), Balance A will also read \( M \cdot g \) because it is only supporting the weight of Balance B and the block. 6. **Conclusion**: - Both spring balances read the same value, which is \( M \cdot g \). Therefore, the true statement about the scale readings is that both scales read \( M \cdot g \). ### Final Answer: Both spring balances read \( M \cdot g \).

To solve the problem, we need to analyze the setup of the two spring balances and the block of mass \( M \) kg hanging from them. ### Step-by-Step Solution: 1. **Understanding the Setup**: - We have two light spring balances. The first spring balance (let's call it Balance A) is hanging from a hook. The second spring balance (Balance B) is hanging from Balance A. - A block of mass \( M \) kg is hanging from Balance B. ...
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