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Water rises to a height of 2 m in a capillary tube. If the tube is tilted 60° from the vertical, to what length in centimeters will the water rise in the tube? (Answer up to 2 decimal places)

Answer :

Final answer:

To find the length to which water will rise in a tilted capillary tube, use the equation: h = (2Tcosθ)/( rρg). Given the height to which water rises and the angle of tilt, you can find the length using the equation. Plug in the values and solve for the length.

Explanation:

Capillary rise is determined by the equation:

h = (2Tcosθ)/( rρg)

where:

  • h is the height to which water rises in the capillary tube
  • T is the surface tension of water
  • θ is the angle that the tube is tilted from the vertical
  • r is the radius of the capillary tube
  • ρ is the density of water
  • g is the acceleration due to gravity

In this case, we know that the water rises to a height of 2 m (200 cm) in the capillary tube, and the tube is tilted 60° from the vertical. We can use the equation to find the length at which the water will rise:

h = (2 × 71.99 × cos(60°)) / (r × 1.0 × 9.8)

For example, if the radius of the tube is 0.01 cm:

h ≈ 2 * 72.75 dyn/cm * 0.01 cm / (1 g/cm³ * 490.5 cm/s²) ≈ 3.00 cm

Therefore, if the tube is tilted 60° from the vertical and has a radius of 0.01 cm, the water will rise to a height of approximately 3.00 cm.

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Rewritten by : Barada