A sperical object of mass 1kg and radius 1 m is falling vertically downward inside a viscous liquid in a gravity free space. At a certain instant the velocity of the sphere is 2 m/s. if the coefficient of viscosity of the liquid is `(1)/(18pi)N-S//m^(2)` then velocity of ball will become 0.5 m/s after a tie

Options

A. In 4 s
B. 2 In 4 s
C. 3 In s
D. 2 In 2 s

Answer

C

Explanation

`m(dv)/(dt)=-6pietarv`
`(1)/(dv)/(dt)=6pi((1)/(18pi))(1)v`
`(dv)/(dt)=-(v)/(3)`
`(dt)/(v)=-(dt)/(3)`
`[Inv]_(2)^(0.5)=[-(t)/(3)]_(t_(1))^(t_(2))`
`In4=(Deltat)/(3)`
`Deltat=3In4`