A metal block of area 0.10m^(2) is connected to a 0.010kg mass via a string that passes over an ideal pulley (considered massless and frictionless) as in figure . A liquid with a film thickness of 0.30mm is placed between the block and the right with a constant speed of 0.085ms^(-1) . Find the coefficient of viscosity of the liquid.

A metal block of area 0.10m^(2) is connected to a 0.010kg mass via a s

1.	A metal block of area 0.10m^(2) is connected to a 0.010kg mass via a string that passes over an ideal pulley (considered massless and frictionless) as in figure . A liquid with a film thickness of 0.30mm is placed between the block and the right with a constant speed of 0.085ms^(-1) . Find the coefficient of viscosity of the liquid.
Answer» Solution :Area of block `A=0.10m^(2)` THICKNESS of film of LIQUID, `l=0.3mm=0.3xx10^(-3)m` Speed of block `v=0.085ms^(-2)` The coefficient of viscosity `eta=?` Mass of sphere `m=0.01kg` Tension in the STRING F=mg `=0.01xx9.8` `=9.8xx10^(-2)N` Shear strain (Modulus of rigidity) `eta=("shear stress")/("strain rate")=(FcancelA)/(vcancelt)` `=(Fl)/(Av)` `=(9.8xx10^(-2)xx0.3xx10^(-3))/(0.1xx0.085)` `=345.88xx10^(-5)` `thereforeeta=3.46xx10^(-3)Pas` `eta=(2)/(9)xx(r^(2)g)/(v_(t))(rho-sigma)` `=(2xx(2XX10^(-3))^(2)xx9.8(8.9xx10^(3)-1.5xx10^(3)))/(9xx6.5xx10^(-2))` `=9.917xx10^(-6+3+2)` `=9.9xx10^(-1)` `=0.99kgm^(-1)s^(-1)`