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Tow sphares of equal masses but radius r...

Tow sphares of equal masses but radius `r_1 and r_2` are allowed to fall in liquid of infinit columm. The ratio of their terminal velocityes are

A

1

B

`r_1 : r_2`

C

`r_2 : r_1`

D

`sqrt(r_1) : sqrt(r_2)`

Text Solution

Verified by Experts

The correct Answer is:
C
As `v_T prop r^2 rho` (neglecting density of liquid) where `rho` = density of material of sphere
Now , `4/3 pi r_1^3 rho_1 = 4/3 pi r_2^3 rho_2 " or " 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`
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