Two identical spring balances S₁ and S₂ are connected one after the ot

Two identical spring balances S₁ and S₂ are connected one after the other and are held vertically as shown in the figure. A mass of 10 kg is hanging from S₂. If the readings on S₁ and S₂ are W₁ and W₂ respectively, then:

[amp_mcq option1=”W₁=5kg and W₂=10kg” option2=”W₁=10kg and W₂=5kg” option3=”W₁=5kg and W₂=5kg” option4=”W₁=10kg and W₂=10kg” correct=”option4″]

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UPSC NDA-1 – 2023

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The correct option is D.

When identical spring balances are connected in series and a mass is suspended from the lower one, the lower balance measures the weight of the suspended mass. The upper balance measures the total tension required to support everything hanging below it, which includes the lower balance (assuming negligible weight for the balance itself) and the suspended mass. Thus, both balances will read the weight of the 10 kg mass.

Spring balances measure force (tension). When used to measure weight under gravity, they are often calibrated to display mass (mass = weight / g). In this setup, the tension in the lower spring (S₂) is equal to the weight of the 10 kg mass. The tension in the upper spring (S₁) is equal to the sum of the tensions from S₂ and the weight of S₂ itself. Assuming the spring balances have negligible weight, S₁ measures the same tension as S₂, which is the weight of the 10 kg mass. If the mass is 10 kg, its weight is approximately 10g N. A spring balance calibrated in kg would read 10 kg for a 10 kg mass under standard gravity.

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