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Q.

Two spherical balls of radius 2r and r both having density $σ$ are tied up with light string and released in a viscous fluid of density $ρ > σ$ with the rope just taut. The tension in rope when spheres attain terminal velocity:

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a

$\frac{8}{3} π r^{3} (ρ - σ) g$

b

$\frac{3}{5} π r^{3} (ρ - σ) g$

c

$\frac{10}{5} π r^{3} (ρ - σ) g$

d

$\frac{5}{3} π r^{3} (ρ - σ) g$

answer is B.

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Detailed Solution

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When the body is moving with terminal velocity

Balancing forces
$M g (\frac{ρ}{σ} - 1) - T - 6 π (2 r) η v = 0$ ...(1)
$m g (\frac{ρ}{σ} - 1) + T - 6 π r η v = 0$ ...(2)

From (1) and (2), we get
$T = (\frac{ρ}{σ} - 1) g = \frac{8}{3} π r^{3} (ρ - σ) g$

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Two spherical balls of radius 2r and r both having density σ are tied up with light string and released in a viscous fluid of density ρ>σ with the rope just taut. The tension in rope when spheres attain terminal velocity: