Class 12 Maharashtra State Board

A horizontal force of 1 N is required to move a metal plate of area 10^-2 m² with a velocity of 2 × 10^-2 m/s, when it rests on a layer of oil 1.5 × 10^-3 m thick. Find the coefficient of viscosity of oil.

The data that can be listed from the question is as follows,

Force F = 1N

$https://latex.codecogs.com/svg.image?\mathrm{Area A = 10^{-2} m^{2}}$

$https://latex.codecogs.com/svg.image?\mathrm{velocity, v = 2 x 10^{-2} m^{2}}$

$https://latex.codecogs.com/svg.image?\mathrm{thickness, y = 1.5 x 10^{-3} m}$

To find, coefficient of viscosity η = ?

Solution -

$https://latex.codecogs.com/svg.image?\mathrm{F = \eta A \frac{dv}{dy}}$

$https://latex.codecogs.com/svg.image?\mathrm{\frac{dv}{dy}} = \mathrm{\frac{2 x 10^{-2}}{1.5 x 10^{-3}}}= \mathrm{\frac{20}{1.5}}$

$https://latex.codecogs.com/svg.image?\mathrm{1 = \eta x 10^{-2} x \frac{20}{1.5}}$

$https://latex.codecogs.com/svg.image?\mathrm{1 = \eta x \frac{20}{150}}$

$https://latex.codecogs.com/svg.image?\mathrm{\eta = \frac{150}{20} = 7.5 Ns/m^{2}}$

The viscosity of the oil is 7.5 Ns/m2

The mass of the earth is 6 x 10²⁴ kg. The distance between the earth and the Sun is 1.5x 10¹¹ m. If the gravitational force between the two is 3.5 x 10²² N, what is the mass of the Sun?