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If the terminal speed of a sphere of gol...

If the terminal speed of a sphere of gold (of density `19.5 g//cm ^3` ) is 0.2 m/s in a viscous liquid of density 1.5 ` g// cm ^3`find the terminal speed of a sphere of silver (of density ` 0.5 g // cm ^ 3 ` ) of the same size in the same liquid

A

`0.4 m//s`

B

`0.133 m//s`

C

`0.1 m//s`

D

`0.2 m//s`

Text Solution

Verified by Experts

The correct Answer is:
C
Terminal speed of spherical body in a viscous liquid is given by
`v_(T) = (2r^(2)(rho - sigma)g)/(9eta)`
where `rho =` density of substance of body.
`sigma =` density of liquid
For given data
`(v_(T)(Ag))/(v_(T)(Gold)) = (rho_(Ag) - sigma_(1))/(rho_(Gold) - sigma_(1))`
`rArr v_(T)(Ag) = (10.5 - 1.5)/(19.5 - 1.5) xx 0.2 = (9)/(18) xx 0.2`
`= 0.1 m//s`
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