if a ball of steel (density `rho=7.8 g//cm^(3)`) attains a terminal velocity of `10 cm//s` when falling in a tank of water (coefficient of viscosity, `eta_(water) =8.5xx10^(-4)`Ps s), then its terminal velocity in glycerine `(rho =1.2 g//cm^(2), eta =13.2 Pa s)` would be nearly

Options

A. `1.6xx10^(-5)cms^(-1)`
B. `6.25xx10^(-4)cms^(-1)`
C. `6.45xx10^(-4)cms^(-1)`
D. `1.5xx10^(-5)cms^(-1)`

Answer

B

Explanation

We know thast `v prop(rho-rho_(0))/(eta)`
`implies(v_(2))/(v_(1))=(rho-rho_(02))/(rho-rho_(01))xx(eta_(1))/(eta_(2))`
or `v_(2)=(7.8-12)/(7.8-1)xx(8.5xx10^(-4)xx10)/13.2`
`=6.25xx10^(-4)cm//s`