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

The velocity of a small ball of mass m and density $\mathrm{\rho }$ when dropped in a container filled with glycerin of density $\sigma$ becomes constant after sometime. The viscous force acting on the ball in the final stage is:-

1. $\mathrm{mg}\left(\frac{\mathrm{\sigma }}{\mathrm{\rho }}\right)$

2. $\mathrm{mg}\left(1+\frac{\mathrm{\sigma }}{\mathrm{\rho }}\right)$

3. $\mathrm{mg}\left(1-\frac{\mathrm{\sigma }}{\mathrm{\rho }}\right)$

4. mg

The velocity of a small ball of mass \(M\) and density \(d\), when dropped in a container filled with glycerine becomes constant after some time. If the density of glycerine is \(\dfrac{d}{2}\) then the viscous force acting on the ball will be:
1. \(\dfrac{3Mg}{2}\)
2. \(2Mg\)
3. \(\dfrac{Mg}{2}\)
4. \(Mg\)

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: