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Q.

A steel ball of radius 0.05cm and density 7.8 g cm3 is dropped into a tank of water. The terminal velocity of the steel ball is (Density of water = 1 g cm3 and viscosity of water=0.001 Pa-s)

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a

3.42 ms1

b

1.81 ms1

c

5.11 ms1

d

3.77 ms1

answer is D.

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Detailed Solution

Given r = 0.05cm =5×104m
Density of ball ρ=7.8gcm3=7.8×103kg/m3
Density of water σ=1gcm3=103kgm3
Coefficient of viscosity, η=0.001Pas=103Pas
  terminal velocity if ball
v=2gr2(ρσ)9η=2×10×(5×104)2(7.8×103103)9×103=3.77ms1

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