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A metal plate of area 0.10m^(2) is conne...

A metal plate of area `0.10m^(2)` is connected to a `0.01 kg` mass via a string that pases over an idial pulley (considered to be frictionless), as shown in the figure. A liquid with a film thickness of `3.0 mm` is placed between the plate and the table. When released the plate moves to the right with a constant speed of `0.085ms^(-1)`. Find the coefficient of vicosity of the liquid.

Text Solution

Verified by Experts

As the metal plate moves with constant velocity.
`mg-T=0impliesT=mg`
If `F` is the vicous force on the plate then
`F=T=mg=0.01xx9.8=9.8xx10^(-2)N`
By Newton's law of viscosity,
`F=etaA(dv)/(dy)`
where `(dv)/(dy)=0.085/(0.3xx10^(-3))=28.3s`
`implies 9.8xx10^(-2)=etaxx00.10xx28.3`
`implies eta=3.8xx10^(-3)Ns//m^(2)`
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