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):

Question

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):

Smart Achievers · Accepted Answer

(2)

$m = \frac{4}{3} π r^{3} ρ m,$ $Keeping m constant, if r is halved, ρ will increased by a factor of 8 .$

$Now, V_{0} \propto r^{2} ρ$

$V_{0}' \propto \frac{r^{2}}{4} (8 ρ) or V_{0}' \propto 2 r^{2} ρ,$

$Dividing, \frac{V_{0}'}{V_{0}} = 2 or V_{0}' = 2 V_{0} or V_{0}' = 2 V$

Solution

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):

1 $v$

2 $2 v$

3 $4 v$

4 $8 v$

Ans.
(2)

$m = \frac{4}{3} π r^{3} ρ m,$ $Keeping m constant, if r is halved, ρ will increased by a factor of 8 .$

$Now, V_{0} \propto r^{2} ρ$

$V_{0}' \propto \frac{r^{2}}{4} (8 ρ) or V_{0}' \propto 2 r^{2} ρ,$

$Dividing, \frac{V_{0}'}{V_{0}} = 2 or V_{0}' = 2 V_{0} or V_{0}' = 2 V$

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Solution

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):

1 v

2 2v

3 4v

4 8v

Ans. (2) m=43πr3ρm, Keeping m constant, if r is halved, ρ will increased by a factor of 8. Now, V0∝r2ρ V0'∝r24(8ρ) or V0'∝2r2ρ, Dividing, V0'V0=2 or V0'=2V0 or V0'=2V