A sperical ball of mass m, radiua r is connected to string of length `(l gt gt r)`. This string is then connected to fixed point and this arrangement allowed to oscillate in a medium whose density is `rho` and viscosity is `eta`. If amplitude of oscillation becomes half of the initial value after n seconds then viscosity of liquid is given by (Assume that resistance force on ball follows stoke's law)

Options

A. `(m)/(pirn)`
B. `(mln(2^(1//3)))/(pirn)`
C. `(mln8)/(pirn)`
D. `(mln2)/(pirn)`

Answer

B

Explanation

`A=A_(0)e^(-b//2mt)b=6pireta`
`(A_(0))/(2)=A_(0)e^(-b//2m.Deltat)`
`ln2=(6pireta)/(2m).n`
`eta=(mln2)/(3pirn)`