A rectangular metal plate has dimensions of `10cmxx20cm`. A thin film of oil separates the plate from a fixed horizontal surface. The separation between the rectangular plate and the horizontal surface is `0.2mm`. An ideal string is attached to the plate and passes over an ideal pulley to a mass `m`. When `m=125gm`, the metal plate moves at constant speed of `5(cm)/(s)`, across the horizontal surface. Then the coefficient of viscosity of oil in `(dyne-s)/(cm^2)` is (Use `g=1000(cm)/(s^2)`)

Options

A. 5
B. 25
C. 2.5
D. 50

Answer

C

Explanation

The coefficient of viscosity is the ration of tangential stress on top surface of film (exerted by block) to that of velocity gradient (vertically downwards) of film. Since mass `m` moves with constant velocity, the string exerts a force equal to `mg` on plate towards right. Hence oil shall exert tangential force `mg` on plate towards left.
`eta=((F)/(A))/(((v-0))/(trianglex))=((125xx100)/(10xx20))/(((5-0))/(0.2))`
`=2.5(dyn e)/(cm^2)`