Two balls A and B have radii in the ratio 1:2. What will be the ra | Filo
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Class 11

Physics

Mechanics

Mechanical Properties of Fluids

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Two balls A and B have radii in the ratio 1:2. What will be the ratio of their terminal velocities in a liquid?

Solution:
Let the radius of the smaller ball

the radius of the bigger ball

Density of the ball's material

Density of liquid

Terminal velocity of the balls is v1 and v2 for the smaller and bigger respectively. 

Volume of the smaller ball

The mass of the ball will be

Volume of the bigger ball

The mass of the ball will be

Upthrust on the smaller ball

Viscous drag force on smaller ball

Weight of the smaller ball

Now, since the balls are moving with terminal velocity, the total upward force will balance its weight 

= 8 \rho V_g= 6\pi \eta 2rv_2= 8\rho _bV_g8\rho V_g+6\pi\eta 2rv_2=8\rho _bV_g\dfrac{ρVg+6πηrv1}{8ρVg+12πηrv2}=\dfrac{1}{8}8\rho V_g+12\pi \eta rv_2=8\rho V_g+48\pi \eta rv_112\pi \eta rv_2=48\pi \eta rv_1v_2=4v_1\dfrac{v_1}{v_2}=\dfrac{1}{4}= 1:4$$
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