Question

Two spheres of equal masses but radii r₁ and r₂ are allowed to fall in a liquid of infinite column. The ratio of their terminal velocities are ____________.

Options

• 1

• r₁ : r₂

• r₂ : r₁

• `sqrt"r"_1 :  sqrt"r"_2`

Answer 1

Two spheres of equal masses but radii r₁ and r₂ are allowed to fall in a liquid of infinite column. The ratio of their terminal velocities are r₂ : r₁.

Explanation:

`"v" prop "r"^2 rho  "(neglecting density of liqwd)"`

`"where"  rho = "density of material of sphere"`

`"now",  4/3 pi "r"_1^3  rho_1`

`= 4/3 pi "r"_2^3  rho_2  Rightarrow rho_1/rho_2 = "r"_2^3/"r"_1^3`

`therefore  "v"_1/"v"_2 ="r"_1^2/"r"_2^2 xx rho _1/rho_2 `

`= "r"_1^2/ "r"_2^2 xx "r"_2^3/ "r"_1^3`

` = "r"_2/"r"_1 `