Question

A ball bearing of radius 20cm and mass of 0.2kg moving through a liquid of viscosity 1.2×10^-6 NSM^-1. What is the terminal velocity?

Answer 1

Given: Radius of bearing $r=20cm,=0.2m$

mass of bearing $m=0.2kg$

Viscosity of liquid $\eta=1.2\times10^{-6} Nsm^{-1}$

To find: Terminal velocity =?

Solution: we know that,

Mass =volume $\times$ density

$0.2=\dfrac{4}{3}\pi(0.2)^3\times$ Density

$\Rightarrow$ Density$\rho=\dfrac{3}{4\pi\times 0.04}$ =5.965kg/$m^3$

Terminal velocity is given by-

$v_t=\dfrac{2gr^2}{9\eta}\rho$

$\Rightarrow v_t=\dfrac{2\times 9.8\times (0.2)^2\times 5.965}{9\times 1.2\times 10^{-6}}$

$\Rightarrow v_t=\dfrac{4.646\times 10^6}{10.8}=0.43\times 10^6ms^{-1}$

Hence the terminal velocity of object is $0.43\times 10^6ms^{-1}$