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The velocity of a small ball of mass 0.3 g and density 8 g/cc when dropped in a container filled with glycerine becomes constant after some time. If the density of glycerine is 1.3 g/cc, then the value of viscous force acting on the ball will be x × 10⁻⁴ N, the value of x is _____. [use g = 10 m/s²]
- 25.00
- 2.50
- 0.25
- 25.125
Correct answer: 25.125
Solution
Ball volume V = m/ρ = 0.3/8 cc = 3.75×10^-8 m³. Buoyant force = Vρ_gly g = 3.75×10^-8×1300×10 = 4.875×10^-4 N; weight = 0.3×10^-3×10 = 30×10^-4 N. Viscous force = weight - buoyancy = 25.125×10^-4 N, so x = 25.125.
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