Q.

Four lead spheres a, b, c & d whose radii 1 cm, 2cm, 3cm, and 4cm respectively are dropped into liquids of coefficients of viscosity 1×10-3 Pa-s, 2×10-5  Pa-s ,6.5×10-3 Pa-s, 15.4×10-3Pa-s.

Arrange the  spheres with their terminal velocity in descending order

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a

a, b, c, d

b

b, c, d, a

c

a, c, d, b

d

c, d, a, b

answer is B.

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Detailed Solution

Terminal velocity is calculated by Vt=2gr2ρb-ρl9η

Vtr2η

For the above values, 

the four spheres' terminal velocities will be proportional to 

121×10-3,222×10-5,326.5×10-3,4215.4×10-3

which is 

1×103, 2×105, 1.38×103, 1.038×103

The terminal velocities are in the order of b, c, d, a.

 

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