Question

If the terminal speed of a sphere of gold (density `=19.5kg//m^3`) is `0.2m//s` in a viscous liquid (density `=1.5kg//m^3`), find the terminal speed of a sphere of silver (density `=10.5kg//m^3`) of the same size in the same liquid
A. `0.4ms^(-1)`
B. `0.133ms^(-1)`
C. `0.1ms^(-1)`
D. `0.2ms^(-1)`

Answer 1

Correct Answer - C
Terminal speed of spherical body in a viscous liquid is given by
`v_T=(2r^2(rho-sigma)g)/(9eta)`
where , `rho` = density of substance of body and
`sigma` = density of liquid
from given data
`(v_T(Ag))/(V_T(Gold))= (rho_(Ag) - sigma_l)/(rho_(Gold)- sigma_l)`
`rArr v_T(Ag) = (10.5-1.5)/(19.5-1.5) xx0.2 = 9/18xx0.2=0.1 ms^(-1)`