A small ball of mass m and density ρ is dropped in a viscous liquid of density ρ0 . After sometime, the ball falls with constant ​velocity

Question

A small ball of mass m and density \(\rho\) is dropped in a viscous liquid of density \(\rho_{0}\). After sometime, the ball falls with constant velocity. The viscous force on the ball is :

(1) \(\operatorname{mg}\left(\frac{\rho_{0}}{\rho}-1\right)\)

(2) \(\operatorname{mg}\left(1+\frac{\rho}{\rho_{0}}\right)\)

(3) \( \operatorname{mg}\left(1-\rho \rho_{0}\right)\)

(4) \(\operatorname{mg}\left(1-\frac{\rho_{0}}{\rho}\right)\)

Answer 1

Correct option is :  (4)  \(\operatorname{mg}\left(1-\frac{\rho_{0}}{\rho}\right)\)

\(\mathrm{mg}-\mathrm{F}_{\mathrm{B}}-\mathrm{F}_{\mathrm{v}}=\mathrm{ma}\)

\(\mathrm{a}=0\) for constant velocity

\(\mathrm{mg}-\mathrm{F}_{\mathrm{B}}=\mathrm{F}_{\mathrm{v}}\)

\(F_{v}=m g-v \ \rho_{0} g=m g-\frac{m}{\rho} \rho_{0} g=m g\left(1-\frac{\rho_{0}}{\rho}\right)\)