The correct statement about the variation of viscosity of fluids with an increase in temperature is:

A metal block of area \(0.10~\text{m}^{2}\) is connected to a \(0.010~\text{kg}\) mass via a string that passes over an ideal pulley (considered massless and frictionless), as in the figure below. A liquid film with a thickness of \(0.30~\text{mm}\) is placed between the block and the table. When released the block moves to the right with a constant speed of \(0.085~\text{m/s}.\) The coefficient of viscosity of the liquid is:

          
1. \(4.45 \times 10^{-2}~\text{Pa-s}\)
2. \(4.45 \times 10^{-3}~\text{Pa-s}\)
3. \(3.45 \times 10^{-2}~\text{Pa-s}\)
4. \(3.45 \times 10^{-3}~\text{Pa-s}\)

A solid sphere, of radius \(R,\) acquires a terminal velocity \(v_1\) when falling (due to gravity) through a viscous fluid having a coefficient of viscosity \(\eta.\)$$ The sphere is broken into \(27\) identical solid spheres. If each of these spheres acquires a terminal velocity, \(v_2\), when falling through the same fluid, the ratio \(\left(\dfrac{v_1}{v_2}\right) \) equals:
1. \(\dfrac{1}{9}\)
2. \(\dfrac{1}{27}\)
3. \(9\)
4. \(27\)

Two small spherical metal balls, having equal masses, are made from materials of densities \(\rho_1\) and \(\rho_2\) such that ${}_{}$\(\rho_1=8\rho_2\) and having radii of \(1\) mm and \(2\) mm, respectively. They are made to fall vertically (from rest) in a viscous medium whose coefficient of viscosity equals \(\eta\) and whose density is \(0.1\rho_2\)${\mathrm{}}_{}$. The ratio of their terminal velocities would be: