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A capillary tube of radius 1 mm is dipped vertically with its lower end into mercury. Surface tension of mercury = 0.465 N/m and contact angle with glass = 135 deg. (a) Find the depression of the mercury column inside the capillary. (b) If the depth dipped into the mercury equals half the depression found in (a), find the angle the mercury surface at the tube end makes with the vertical.
- h = 4.94 mm; angle = 45 deg from vertical (i.e. contact angle effectively 90 deg)
- h = 9.88 mm; angle = 30 deg from vertical
- h = 2.47 mm; angle = 60 deg from vertical
- h = 4.94 mm; angle = 60 deg from vertical
Correct answer: h = 4.94 mm; angle = 45 deg from vertical (i.e. contact angle effectively 90 deg)
Solution
Standard capillary formula gives the depression magnitude. When the dip depth is only half this value, mercury cannot depress to its natural value, so the meniscus assumes a less curved shape with a new effective contact angle. Setting the new depression equal to the available depth and solving for the new angle gives the surface inclination.
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