A lead sphere of `1.0 mm` diameter and relative density `11.20` attains a terminal velocity of `0.7 cm s^(-1)` in a liquid of relative density `1.26`.
Determine the coefficient of dynamic viscosity of the liquid.

Options

A. `0.45N//m^(2)`
B. `0.85N//m^(2)`
C. `0.56N//m^(2)`
D. `0.77N//m^(2)`

Answer

D

Explanation

If `rho_(w)`is the density of water, then the density of the lead sphere and the density of the liquid are given by
`rho_(0)=11.20rho_(w)` and `rho=1.26rho_(w)`
Thus, the equation `T=2pisqrt(l/(2g))` may be written as
`eta=2/9 (r^(2))/v(11.20-12.6)rho_(w)g`
Here `r=0.5xx10^(-3)m, v=0.7xx10^(-2)ms^(-1), g=9.8ms^(-12),`
`rho_(w)=10^(3)kg//m^(3)`
`eta=2/9((0.5xx10^(-3))/(0.7xx10^(-2)))(11.20-1.26)(10^(3))(9.8)`
`=0.77Ns//m^(2)`