Question

The largest and the smallest balls used in the experiment are with diameter 9.52 mm, and 2.38 mm respectively. For a glycerin with viscosity 1.5 Pa.s, what is the time necessary for each ball to rich a velocity 99% of the terminal velocity? Density of the ball material is given in the text. Round the result to three decimal places.

Answer 1

Answer

given,

largest diameter of  balls = 9.52 mm = 0.00476 m

                                 radius = 0.00476

smallest diameter of ball = 2.38 mm = 0.00238 m

                                 radius = 0.00119

viscosity = 1.5 Pa.s

density of the ball = 1.42 g/cm

$F = 6\pi \eta r V_t$

$F = \dfrac{mv}{t}$

$F = \dfrac{\dfrac{4}{3}\pi\ r^3\times (\rho-\sigma) \times 0.99 V_T}{t}$

$6\pi \eta r V_t = \dfrac{\dfrac{4}{3}\pi\ r^3\times rho \times 0.99 V_T}{t}$

$t = \dfrac{\dfrac{4}{3}\pi\ r^3\times rho \times 0.99 V_T}{6\pi \eta r V_t}$

$t= \dfrac{0.22 r^2 (\rho-\sigma) }{\eta}$

for small balls

$t= \dfrac{0.22\times 0.00119^2 (1460-1300)}{1.5}$

t = 0.033 ms

for larger ball

$t= \dfrac{0.22\times 0.00476^2 (1460-1300)}{1.5}$

t = 0.531 ms