InterviewSolution
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InterviewSolution
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A metal ball `B_(1)` (density `3.2g//"cc")` is dropped in water, while another metal ball `B_(2)` (density `6.0g//"cc")` is dropped in a liquid of density `1.6g//"cc"`. If both the balls have the same diameter and attain the same terminal velocity, the ratio of viscosity of water to that of the liquid isA. 2B. 0.5C. 4D. indeterminate due to insufficient data |
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Answer» Correct Answer - B The terminal velocity of the bodyof radius r, density `rho` falling through a medium of density `alpha` is given by `v=2/9(r^(2)(rho-sigma_(water)g))/(eta)` where `eta` is the coefficient of viscosity of the medium `thereforevB_(1)=2/9(r_(B_(1))^(2))/(eta_("liquid"))(rho_(B_(2))sigma_("water"))g" "..(i)` and `v_(B_(2))=(2)/(9)(r_(B_(1))^(2))/(eta_("liquid"))(rhoB_(2)-sigma_("liquid"))g" "...(ii)` where the subscripts `B_(1)` and `B_(2)` respectively. `because r_(B_(1))=r_(B_(2)) and v_(B_(1))=v_(B_(2))" "` (Given) Substituting these values in (i) and (ii), we get `(eta_("water"))/(eta_("liquid"))=((rho_(B_(1))-sigma_("water")))/((rho_(B_(2))-sigma_("liquid")))` Substituting the given values, we get `(eta_("water"))/(eta_("liquid"))=((3.2-1))/((6.0-1.6))(because` Density of water `=1 g cm^(-3))` `(2.2)/(4.4)=0.5` |
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