1. Tardigrade
  2. Question
  3. Physics
  4. A spherical ball of density ρ and radius 0.003 m is dropped into a tube containing a viscous fluid. If the viscosity of the fluid =1.260 N m -2 and its density is ρL= ρ / 2=1260 kg m -3, then find the terminal speed (in cm / s ) of the ball. (g=. Acceleration due to gravity .=10 m s -2)

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Q. A spherical ball of density $\rho$ and radius $0.003 \,m$ is dropped into a tube containing a viscous fluid. If the viscosity of the fluid $=1.260 \,N m ^{-2}$ and its density is $\rho_{L}=$ $\rho / 2=1260 \,kg \, m ^{-3}$, then find the terminal speed (in $cm / s$ ) of the ball. $\left(g=\right.$ Acceleration due to gravity $\left.=10 \, m \, s ^{-2}\right)$

Mechanical Properties of Fluids

Solution:

$M a=F_{\text {net }}=M g-B-6 \pi \eta r v$
At $v=v_{T}, a=0$
$\Rightarrow M g-B=6 \pi \eta r v_{T}$
$\Rightarrow v_{T}=\frac{\frac{4}{3} \pi r^{3}\left[\rho-\frac{\rho}{2}\right] g}{6 \pi r \eta}=2 \,m / s$