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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

83πr3(ρ−σ)g

b

35πr3(ρ−σ)g

c

105πr3(ρ−σ)g

d

53πr3(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
Mg(ρσ−1)−T-6π(2r)ηv=0...(1)
mg(ρσ−1)+T-6πrηv=0...(2)

From (1) and (2), we get 
T=(ρσ−1)g=83πr3(ρ−σ)g

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