A small metallic sphere of diameter 2 mm and density 10.5 ~g / cm ³ is dropped in glycerine having viscosity 10 Poise and density 1.5 ~g / cm ³ respectively. The terminal velocity attained by the sphere is _ _ _ _ cm / s . ( = 22 7 and g=10 ~m / s ² )

Step-by-step solution

Using Stokes' Law for terminal velocity: v_t = 2r^2g( _s - _f) 9 . Given: r = 0.1 cm, g = 1000 cm/s², _s = 10.5 g/cm³, _f = 1.5 g/cm³, η = 10 Poise = 10 g/(cm⋅s). Substituting: v_t = 2 (0.1)^2 1000 (10.5 - 1.5) 9 10 = 2 0.01 1000 9 90 = 180 90 = 2.0 cm/s.