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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

m=43πr3ρKeeping m constant, if r is halved, ρ will increased by a factor of 8. Now, v0∝r2ρNew velocity is v0'∝r24(8ρ)  or  v0'∝2r2ρ Dividing, v0'v0=2  or  v0'=2v0 or  v0'=2v
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