Question 429: Properties of Matter

Question

Consider two solid spheres P and Q each of density 8 gm cm
–3
and diameters 1 cm and 0.5 cm, respectively. Sphere P is dropped into a liquid of density 0.8 gm cm
–3
and viscosity $$\eta $$ = 3 poiseulles. Sphere Q is dropped into a liquid of density 1.6 gm cm
–3
and viscosity $$\eta $$ = 2 poiseulles. The ratio of the terminal velocities of P and Q is

Accepted Answer

Terminal velocity is given by
$${v_T} = {2 \over 9}{{{r^2}} \over \eta }(d - ho )g$$
$${{{v_P}} \over {{v_Q}}} = {{r_P^2} \over {r_Q^2}} 	imes {{{\eta _Q}} \over {{\eta _P}}} 	imes {{(d - {ho _P})} \over {(d - {ho _Q})}}$$
$$ = {\left( {{1 \over {0.5}}} ight)^2} 	imes \left( {{2 \over 3}} ight) 	imes {{(8 - 08)} \over {(8 - 1.6)}} = 4 	imes {2 \over 3} 	imes {{7.2} \over {6.4}} = 3$$

Properties of Matter

Integer / Numeric Answer Type