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If a ball of steel density (rho=7.8gcm^(...

If a ball of steel density (`rho=7.8gcm^(-3)`) attains a terminal velocity of `10cms^(-2)` when falling in a tank of water (coefficient of viscoity `eta_("water")=8.5xx10^(-4)Pa.s`) then its terminal velocity in glycerine `(rho=12gcm^(-3),eta=13.2Pa.a)` would be nearly.

A

`6.25 xx 10^(-4)cms^(-1)`

B

`6.45 xx 10^(-4) cms^(-1)`

C

`1.5 xx 10^(-5) cm//s`

D

`1.6 xx 10^(-5) cms^(-1)`

Text Solution

Verified by Experts

The correct Answer is:
A
`V_rhog = 6pietarv + vrho_(l)g`
`Vg(rho - rho_(l)) = 6pietarv`
`Vg(rho - rho_(l)) = 6pieta'rv'`
`V'eta' = ((rho - rho_(l)'))/((rho - rho_(l))) xx (veta)/(eta')`
`= ((7.8 xx 1.2))/((7.8 - 1)) xx (10 xx 8.5 xx 10^(-4))/(13.2)`
`v' = 6.25 xx 10^(-4) cm//s`.
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