Question

Solution a empty glass test tube is floted vertically in water depth 5 cm. Now on introducing a8cm liquid column in the tube its depth water is furthe increase by 4 cm now if the empty test tube is allow to float vertically in liquid 5cm of the tube is seen in air, find the total length of the tube

Answer 1

Answer on Question #71162-Physics-Mechanics-Relativity

1. Solution a empty glass test tube is floated vertically in water depth 5 cm.

2. Now on introducing a 8 cm liquid column in the tube its depth water is further increase by 4 cm.

3. Now if the empty test tube is allow to float vertically in liquid 5 cm of the tube is seen in air, find the total length of the tube

Solution

1.

$$\rho_{T} g A h = \rho_{\text{Water}} g A (5)$$ $$\rho_{T} = \frac{5 \rho_{\text{Water}}}{h}.$$

2.

$$\rho_{L} g A (8) = \rho_{\text{Water}} g A (4)$$ $$\rho_{L} = \frac{1}{2} \rho_{\text{Water}}.$$

3.

$$\rho_{T} g A h = (h - 5) \rho_{L} g A$$ $$\frac{5 \rho_{\text{Water}}}{h} g A h = (h - 5) \frac{1}{2} \rho_{\text{Water}} g A$$ $$5 = (h - 5) \frac{1}{2}$$ $$h - 5 = 10$$ $$h = 15 \text{ cm}.$$

Answer: 15 cm.

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