Q.

A spherical ball falls through viscous medium with terminal velocity V. If this ball is replaced by another ball of the same mass but half the radius, then the terminal velocity will be  (neglect the effect of buoyancy.)

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a

v

b

2v

c

4v

d

8v

answer is B.

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Detailed Solution

At terminal velocity mg = 6πηrVT. For constant mass, VT ∝1r.Therefore, VT"VT = rr2 ⇒VT" = 2VT = 2V
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A spherical ball falls through viscous medium with terminal velocity V. If this ball is replaced by another ball of the same mass but half the radius, then the terminal velocity will be  (neglect the effect of buoyancy.)