In the measurement of viscosity of liquids using terminal velocity experiment, spherical balls of same radius but having different densities are used. The variation of the terminal velocity ($v$) with the ratio of density of spherical ball ($\sigma$) to density of the liquid ($\rho$), is best represented by :
Answer: (A) see figure
Terminal velocity (Stokes' law):
$$v = \frac{2r^2(\sigma - \rho)g}{9\eta} = \frac{2r^2\rho g}{9\eta}\left(\frac{\sigma}{\rho} - 1\right)$$
For balls of the same radius, $v$ is a straight line in $\dfrac{\sigma}{\rho}$ that becomes zero at $\dfrac{\sigma}{\rho} = 1$ and increases linearly beyond it. (For $\sigma < \rho$ the ball does not sink, so there is no falling terminal velocity to measure.)
This matches option (1).
Solution by Sreeraj P, M.Sc Physics