Write the formula of initial acceleration of sphere falling in a viscous medium and derive the formula of its terminal velocity from it .

Explanation

Initial acceleration ,
`a_(o)=((rho-sigma)g)/(rho)`
In equation , `v=v_(t)andF=0`
`0=(4)/(3)pir^(3)g(rho-sigma)-6pietarv_(t)`
`therefore(6pietar)v_(t)=(4)/(3)pir^(3)g(rho-sigma)`
`thereforev_(t)=(2)/(9)(r^(2)g(rho-sigma))/(eta)`
Hence ,terminal velocity `v_(t)` of small sphere in viscous medium is ,
(i) Proportional to the square of radius of sphere `v_(t)propr^(2)`
(ii) Proportional to the difference of densities of sphere and fluid `v_(t)prop(rho-sigma)`