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 is ____ cm/s.
(π=22/7 and g=10 m/s²)

Solution

Physics sir · 4 steps

At terminal velocity the forces balance, so use vₜ = 2r²(ρ-σ)g/9η in CGS units.

1. Forces balance. At terminal velocity the weight is balanced by the buoyant force plus the Stokes drag 6πη r v. The π appears on both sides of this balance and cancels, so the given value of π is never used.

   vₜ = 2r²(ρ-σ)g/9η

2. Use CGS units. Poise is a CGS unit, so keep everything in CGS. The radius is half the diameter: r = 1 mm = 0.1 cm. Also ρ - σ = 10.5 - 1.5 = 9 g cm⁻³, g = 1000 cm s⁻² and η = 10 P.
3. Put in numbers. vₜ = (2 × (0.1)² × 9 × 1000)/(9 × 10) = 180/90 = 2 cm s⁻¹.
4. So. The terminal velocity is 2.0 cm s⁻¹, which is option (d).

The idea to keep. Terminal velocity grows with r² and with the density difference (ρ-σ). When viscosity is given in poise, work fully in CGS and use the radius, not the diameter.

Answer from the NTA final answer key. Solution by PrepWiser.