Question

Two small spherical metal balls, having equal masses, are made from materials of densities `rho_1` and`rho_2  (rho_1 = 8rho_2)` and have radii of 1 mm and 2 mm, respectively, they are made to fall vertically (from rest) in a viscous medium whose coefficient of viscosity equals `eta` and whose density is `0.1rho_2` The ratio of their terminal velocities would be, ____________.

Options

• `79/36`

• `79/72`

• `19/36`

• `39/72`

Answer 1

Two small spherical metal balls, having equal masses, are made from materials of densities `rho_1` and`rho_2  (rho_1 = 8rho_2)` and have radii of 1 mm and 2 mm, respectively, they are made to fall vertically (from rest) in a viscous medium whose coefficient of viscosity equals `eta` and whose density is `0.1rho_2` The ratio of their terminal velocities would be, `79/36`.

Explanation:

`"Terminal velocity," "v"_"T"= 2/9 "r"^2/eta (rho - sigma)"g"`

`therefore "v"_("T"_1) = (2 xx 1^2)/(9eta) (rho_1 - 0.01  rho_2)"g"`

`= 2/(9eta) (8rho_2 - 0.1  rho_2)g`

`therefore "v"_("T"_2) = 2/(9eta)(7.9)"g"`   .....(i)

`therefore "v"_("T"_1) = (2 xx 2^2)/(9eta) (rho_2 - 0.1  rho_2)"g"`

`therefore "v"_("T"_2) = 8/(9eta)(0.9rho)"g"`   .....(ii)

`therefore "v"_("T"_1)/"v"_("T"_2) = 7.9/(4(0.9)) = 79/36`