Fluid Mechanics

JEE Main level, single correct, medium

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Question 182 of 192

The velocity of a small ball of mass mm and density d1{d}_{1}, when dropped in a container filled with glycerine, becomes constant after some time. If the density of glycerine is d2{d}_{2}, then the viscous force acting on the ball, will be

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Answer: (B) mg(1−d2d1)mg\left(1-\dfrac{{d}_{2}}{{d}_{1}}\right)

At the time of terminal velocity ball is in equilibrium i.e. Fg=Fb+Fv{F}_{g}={F}_{b}+{F}_{v}
⇒Fv=Fg−Fb\Rightarrow {F}_{v}={F}_{g}-{F}_{b}
⇒Fv=mg−d2md1g\Rightarrow {F}_{v}=mg-{d}_{2}\dfrac{m}{{d}_{1}}g
⇒mg(1−d2d1)\Rightarrow mg\left(1-\dfrac{{d}_{2}}{{d}_{1}}\right)

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