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A metal sphere of radius 1 mm and mass 50 mg falls vertically in glycerine. Find (a) the viscous force exerted by the glycerine on the sphere when the speed of the sphere is 1 cm s-1, (b) the hydrostatic force exerted by the glycerine on the sphere and (c) the terminal velocity with which the sphere will move down without acceleration. Density of glycerine = 1260 kg m-3 and its coefficient of viscosity at room temperature = 8.0 poise.

A metal sphere of radius 1 mm and mass 50 mg falls vertically in glycerine. Find (a) the viscous force exerted by the glycerine on the sphere when the speed of the sphere is 1 cm s-1, (b) the hydrostatic force exerted by the glycerine on the sphere and (c) the terminal velocity with which the sphere will move down without acceleration. Density of glycerine = 1260 kg m-3 and its coefficient of viscosity at room temperature = 8.0 poise.

Grade:11

1 Answers

Kevin Nash
askIITians Faculty 332 Points
6 years ago
Sol. a) Viscous force = 6πηrv b) Hydrostatic force = B = (4/3) πr3σg c) 6πη rv + (4/3) πr3σg = mg v = 2/g r2 (p - σ)/ η ⇒ 2/g r2 (m/(4/3)πr3)g/n

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