A small metallic sphere of diameter 2 mm and density 10.5 g/cm³ is dropped in glycerine having viscosity 10 Poise and density 1.5 g/cm³ respectively. The terminal velocity attained by the sphere i $s ________$ cm/s.
(π = 22/7 and g = 10 m/s²)

Question

A small metallic sphere of diameter 2 mm and density 10.5 g/cm³ is dropped in glycerine having viscosity 10 Poise and density 1.5 g/cm³ respectively. The terminal velocity attained by the sphere i $s ________$ cm/s.

(π = 22/7 and g = 10 m/s²)

G1 Physics · Accepted Answer

For a small sphere moving through a viscous liquid, Stokes' law gives the terminal speed v(T) = 2r²g[ρ(sphere)-ρ(liquid)]/(9η). Diameter is 2 mm, so radius is r = 1 mm = 0.1 cm. Use CGS units consistently: g = 10 m/s² = 1000 cm/s², ρ(sphere) = 10.5 g/cm³, ρ(liquid) = 1.5 g/cm³, η = 10 Poise. Therefore, v(T) = [2(0.1)²(1000)(10.5-1.5)]/ (9×10) = [2×0.01×1000×9]/90 = 2 cm/s. Correct option: A.

A small metallic sphere of diameter 2 mm and density 10.5 g/cm³ is dropped in glycerine having viscosity 10 Poise and density 1.5 g/cm³ respectively. The terminal velocity attained by the sphere i s ________ cm/s. (π = 22/7 and g = 10 m/s²)