This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
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To determine the height the water is raised by capillary action, we use the capillary rise formula: h = (2 )/( g r) where: • h is the height of the liquid column • is the surface tension • is the contact angle (for water in a clean glass tube, ≈ 0^, so = 1) • is the density of the liquid • g is the acceleration due to gravity • r is the radius of the capillary tube Step 1: Convert all given values to SI units. Given: • Radius, r = 0.5 mm = 0.5 × 10^-3 m • Surface tension, = 75 dyne cm^-1 • Acceleration due to gravity, g = 9.8 m/s^2 • Density of water, = 1000 kg/m^3 Convert surface tension from dyne/cm to N/m: We know that 1 dyne = 10^-5 N and 1 cm = 10^-2 m. = 75 dynecm × 10^-5 N1 dyne × 1 cm10^-2 m = 75 × 10^-510^-2 Nm = 75 × 10^-3 Nm Step 2: Substitute the values into the capillary rise formula. Assuming the contact angle = 0^, so = 1. h = 2 × (75 × 10^-3 N/m) × 1(1000 kg/m^3) × (9.8 m/s^2) × (0.5 × 10^-3 m) Step 3: Calculate the height h. h = 0.15 N/m1000 × 9.8 × 0.0005 kg/(m^2s^2) · m h = 0.15 N/m4.9 N/m h ≈ 0.030612 m Step 4: Convert the height to centimeters. h = 0.030612 m × 100 cm1 m h ≈ 3.06 cm Comparing this result with the given options: (a) 3.06 cm (b) 6.12 cm (c) 1.53 cm (d) 9.42 cm (e) None of the above The calculated height matches option (a). The final answer is 3.06 cm. That's 2 down. 3 left today — send the next one.