Consider the system shown in figure. Two spherical balls A and B of same volume and densities ρ, ρ8 are connected by a pulley as shown. Ball A is completely submerged in liquid of density ρ4 where ball B is in air, if the terminal velocity of ball A is kρVgπηr find the value of 48k?(V is volume of ball and η is coefficient of viscosity, r is radius of ball)?

F.B.D of ball A T+Fv+FB=mg (For Terminal vel) T=ρ8×V0g vt=5ρVg48πnr K=548×48, K=5.

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Consider the system shown in figure. Two spherical balls A and B of same volume and densities $ρ, \frac{ρ}{8}$ are connected by a pulley as shown. Ball A is completely submerged in liquid of density $\frac{ρ}{4}$ where ball B is in air, if the terminal velocity of ball A is $\frac{k ρ V g}{π η r}$ find the value of 48k?
(V is volume of ball and $η$ is coefficient of viscosity, r is radius of ball)?

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answer is 5.

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Detailed Solution

F.B.D of ball A

$T + F_{v} + F_{B} = m g (F o r Terminal vel) T = \frac{ρ}{8} \times V_{0} g$

$v_{t} = \frac{5 ρ V g}{48 π n r} K = \frac{5}{48} \times 48, K = 5.$

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